LAMINAR FLAME PROPAGATION IN MIXTURES WITH COMPOSITIONAL

STRATIFICATION AT SMALL LENGTH SCALES

BY

DAVID P. SCHMIDT

THESIS

Submitted in partial fulfillment of the requirements

for the degree of Master of Science in Mechanical Engineering

in the Graduate College of the

University of Illinois at Urbana-Champaign, 2011

Urbana, Illinois

Adviser:

Associate Professor Dimitrios C. Kyritsis

ii

Abstract

The behavior and structure of laminar hydrocarbon flames which propagate parallel to the

direction of a periodic gradient of mixture composition was studied both experimentally, using a specially

designed burner, and computationally, using a planar numerical model. The variations in local mixture

composition led to the formation of wrinkled flames, the structure of which were dependent on both

chemical and physical parameters of the particular flame configuration. A qualitative study using

chemiluminescence imaging of stratified methane and propane flames was conducted to characterize their

response to variations in overall mixture composition, strength and length scale of the stratification, and

flow field velocity.

A two-dimensional numerical study was performed to assess the abilities of reduced global

kinetic models to predict the behavior of stratified flames in comparison to computations performed using

detailed mechanisms. It was observed that the reduced kinetic models display a lower limit of

stratification length scale, which is on the order of the laminar flame thickness, below which accurate

prediction of flame behavior is no longer possible. Under these conditions, the computed flames were

observed to undergo a deformation which was much larger than the wrinkling imposed by the

compositional variation, and was unsteady in time. Further analysis of these deformed flames suggested

that a potential cause of this behavior was a failure of the reduced kinetics to capture the increase in local

reaction rate attributed to stratification, and the inability of the driving reactions to counterbalance the

incoming mass flux of fuel led to destabilization of the flame front.

A preliminary analysis of the local stretch rates of the wrinkled flames was also conducted, and it

was observed that even with a uniform incoming flow field, variations in mixture composition were

capable of stretching the flames. The stretch behavior observed was one of alternating flame stretch and

flame compression, which reached very large magnitudes over short distances.

iii

Acknowledgements

First and foremost, I would like to express my gratitude to Professor Dimitrios Kyritsis, who has

provided an endless amount of advice and encouragement in my work. Moreover, the enthusiasm with

which Dimitri approaches all aspects of research has inspired my own work, which I could never have

completed on my own. I would also like to extend my thanks to Taekyu Kang, whose work laid the

foundation for my project, and who was always available to provide valuable insight and feedback.

I am also grateful to my fellow labmates: Ben Wigg, Farzan Kazemifar, Sangkyoung Lee,

Michael Pennisi, David Tse, Dino Mitsingas, and Chris Evans, for their constant willingness to help with

anything at any time. They made the many hours of working a much more enjoyable experience, and

provided a depth of expertise which is greatly appreciated.

Last but certainly not least I would like to acknowledge the support of my family and friends,

who have helped me stay focused on completing this work, and provided an invaluable outlet for all of

the associated stress. I cannot thank everyone enough for their constant encouragement and support.

iv

Table of Contents

Chapter 1: Introduction .......................................................................................................................... 1

1.1 Stratified Combustion Applications ..................................................................................................... 1

1.2 Previous Research in Stratified Combustion ....................................................................................... 1

1.2.1 Edge Flames......................................................................................................................... 2

1.2.2 Flame Front Propagation in Stratified Media ..................................................................... 3

1.3 Combustion Instabilities ...................................................................................................................... 5

1.4 Motivation for the Thesis ..................................................................................................................... 7

Chapter 2: Apparatus and Computational Model ................................................................................ 8

2.1 Parallel Flame Stratification................................................................................................................. 8

2.2 Experimental Flame Imaging ............................................................................................................. 10

2.2.1 Micro-Slot Burner .............................................................................................................. 10

2.2.2 Mixture Flow Control ........................................................................................................ 11

2.2.3 Optical Setup ...................................................................................................................... 12

2.3 Computational Model ........................................................................................................................ 13

2.3.1 Domain and Boundary Conditions .................................................................................... 13

2.3.2 Solver Configuration and Initial Conditions ..................................................................... 15

2.3.3 Reduced Kinetic Mechanisms ............................................................................................ 16

2.3.4 Detailed Kinetic Mechanisms ............................................................................................ 17

Chapter 3: Experimental and Computational Results ....................................................................... 19

3.1 Stratified Flame Structure .................................................................................................................. 19

3.1.1 Radical Natural Chemiluminescence Imaging .................................................................. 19

3.1.2 Flame Simulation with Reduced Chemistry ....................................................................... 26

3.1.3 Flame Simulation with Detailed Chemistry ....................................................................... 31

3.2 Flame Liftoff Analysis ....................................................................................................................... 35

3.2.1 Flame Front Deformation with Reduced Chemistry .......................................................... 35

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3.2.2 Qualitative Considerations ................................................................................................ 37

3.2.3 Flame Zone Analysis .......................................................................................................... 40

3.3 Flame Stretch ..................................................................................................................................... 47

3.3.1 Theoretical Considerations ................................................................................................ 47

3.3.2 Flame Stretch Computations .............................................................................................. 49

Chapter 4: Conclusions and Recommendations ................................................................................. 54

4.1 Concluding Remarks .......................................................................................................................... 54

4.1.1 Stratified Flame Structure .................................................................................................. 54

4.1.2 Flame Liftoff Variation ...................................................................................................... 55

4.1.3 Flame Stretch Rates ........................................................................................................... 56

4.2 Recommendations for Further Study ................................................................................................. 57

References ............................................................................................................................................... 59

Appendix A: Kinetic Mechanisms Used in Computations ................................................................. 62

A.1 Propane_Nox_HighT Mechanism ..................................................................................................... 62

A.2 Modified GRI 3.0 Methane Mechanism ........................................................................................... 68

A.3 ERC N-Heptane Mechanism ............................................................................................................. 76

1

Chapter 1: Introduction

The work presented in this thesis is focused primarily on the propagation of flames in

compositionally stratified media. This chapter provides a brief overview of the relevance and background

of study in this field. The first section considers practical applications in which stratification is often

encountered. The second section is a review of previous research which has been conducted on stratified

flames, beginning with the special case of edge flames, and continuing to more general cases of

inhomogeneous combustion. Because the presence of stratification can lead to the development of flame

instabilities, an overview of classical instability modes is also included. Concluding this chapter is an

outline of the work to be presented in the subsequent chapters.

1.1 Stratified Combustion Applications

While much of the traditional combustion theory addresses either a purely premixed flame or a fully-

nonpremixed diffusion flame, in practice, combustion usually occurs in a mode which is between these

two extremes. Internal combustion engines have traditionally been classified into two categories. Spark-

ignition engines mix air and fuel prior to induction into the cylinder, and it is typically assumed that

combustion occurs purely within the premixed regime. In diesel engines, the fuel spray ignites on contact

with the hot in-cylinder gases, and a diffusion flame develops. Newer engine technologies, such as the

direct-injection-spark-ignition (DISI) engine, rely on combustion which occurs in a partially premixed

mode. Not only is the combustion mixed-mode, but variation of the fuel injection angle and air induction

scheme can substantially impact the in-cylinder mixture formation, and hence the degree of premixed

combustion [1].

In the area of gas turbine combustors, which are used for aerospace propulsion as well as stationary

power generation, stratified combustion allows for operation outside the standard range of air/fuel ratio

conditions while keeping emissions to an acceptably low level. Lean-burn gas turbines have been the

subject of substantial research because they offer reduced fuel consumption. Excess oxygen in these

combustion environments, however, lends to the formation of elevated level of NOx, which is undesirable.

Stratified approaches to the combustion process, such as rich-burn, quick-mix, lean-burn (RQL) vortex

combustors allow for minimization of NOx production whilst simultaneously minimizing the carbon

monoxide emissions from the rich-burn regime [2].

In the field of fire research, understanding of stratified flame propagation is required to develop a

better knowledge of the mechanisms of fire spread, as the combustion mode is inherently stratified.

2

Combustion of solid fuels, as in most fires, occurs in multiple phases: pyrolysis, gas-phase combustion,

and char-combustion. During the pyrolysis phase, volatile gases are released from the solid fuel non-

uniformly, creating a stratified mixture into which the spreading flame propagates. Extensive research has

been performed to model how the composition and variation of the surrounding fuel supply impacts the

spread rate of an unsteady fire line [3]. Pyrolysis and stratified combustion of solid fuel volatiles is also

the driving mechanism in gasification processes. Partial combustion of the solid fuel is used to provide

heat which drives the pyrolysis of additional solids, producing a combustible gas which can be used for

fuel. Gasification processes have gained renewed interest, due to their ability to process a large variety of

feedstock materials, including bio-based solid fuels, making them ideal sources of alternative energy

production [4].

1.2 Previous Research in Stratified Combustion

1.2.1 Edge Flames

One special case of stratified combustion that has been of particular interest is the edge flame,

which is characterized by its propagation through an inhomogeneous media, perpendicular to the direction

of compositional variation. A comprehensive review of the theory and phenomenology of edge flames has

been compiled by Buckmaster [5].

Edge flames are distinct from classical deflagrations in that they are 2-dimensional constructs,

and because of this the concepts of the planar reaction zone and one-dimensional flame speed cannot be

applied. Additionally, due to the inhomogeneity of the combusting mixture, edge flames are not restricted

to propagation in the positive direction; they can either advance into the unburned mixture, or retreat

downstream. A commonly observed structure in edge flames is the tribrachial flame, in which the leading

edge is clearly defined by two premixed deflagrations which develop as the result of nonuniformity in the

unburned gas. One of the premixed flames is fuel-rich, whereas the other is fuel lean. Downstream of

these leading flame fronts, the unburned excess fuel and oxidizer diffuse into one another, creating a

trailing diffusion flame which forms the third component of the tribrachial structure.

In contrast to deflagrations, the propagation rate of edge flames depends not only on the local

equivalence ratio, but also on the local gradient of composition. For premixed flames, the laminar flame

speed is a function solely of the unburned gas composition. A study of the liftoff heights of propane edge

flames showed that flames with a slight gradient of composition propagated upstream more rapidly than

when the mixture was uniform [6]. ysis y u i an showed that the propagation rate of edge

flames is also dependent on the Lewis number, similar to the case of stretched premixed flames. As the

3

Lewis number decreases, the curvature of the flame front induced by transverse gradients of composition

led to an increase in the propagation rate [7].

Variation in mixture composition can lead to the development of oscillating instabilities in edge

flames, in which the flame alternates between periods of advance and retreat. The typical mode of this

instability is for the flame to retreat gradually, during which time nearly all of the combustion is in the

form of a diffusion flame. The flame then advances in a rapid burst, where it behaves similarly to a

premixed deflagration [5, 8]. These oscillations can become very pronounced under the proper

circumstances. Edge flames propagating in small diameter circular tubes were observed to develop a

steady unstable mode of propagation in which the flame periodically extinguished and reignited [9].

Experimental work by Wason et al. focused on the interaction of two edges flames of differing

composition brought into close proximity of one another. The liftoff heights of the two individual flames

varied with the local composition, where the flame nearer to stoichiometry exhibited a smaller liftoff

height. As the flames were drawn closer to one another, the liftoff height and overall structure of each

flame began to change due to aerodynamic interactions of the flow fields surrounding the two flames.

Decreasing the equivalence ratio gradients caused the two flames to broaden and eventually merge,

forming a single edge flame with a bifurcated liftoff height, which eventually became a single uniform

edge flame at zero gradient [10]. Further study of the same flames revealed that the previously observed

interactions between neighboring edge flames were purely hydrodynamic in nature. No significant

transport of chemical radicals or thermal energy between the flames was observed, and fluctuations in

flame speed and scalar dissipation rate were found to result only from direct contact between the

individual flame flow fields [11].

1.2.2 Flame Front Propagation in Stratified Media

Work in steady stratified combustion has recently become an area of interest outside of the

traditional edge flame configuration. Early work by Ishikawa [12] used schlieren imaging of methane-air

flames in a diffusion-layer combustor to measure the propagation speeds of flames in mixing media.

Results showed that in the stratified media, ignition occurred only in regions of locally stoichiometric

composition, and that the flame speed near the ignition region was accelerated by unsteady heat flux in

the unburned gas caused by mixture inhomogeneity. However there was no clear correlation between the

composition and flame speed, as the experiment did not include a means of measuring species

4

concentrations, and the physical dimensions of the combustor were not sufficiently large to allow for

steady flame propagation following ignition.

A numerical study of methane counterflow diffusion flames used a periodic, time-varying

oscillation of equivalence ratio to observe unsteady flame response. Frequency response analysis showed

that when the frequency of compositional modulation was low, the flame oscillated in a quasi-steady

manner, but increasing the frequency attenuated the oscillation amplitude and introduced a phase shift.

This behavior was attributed to the fact that faster changes in the mixture result in larger gradients of

composition across the flame, increasing the local diffusive species flux, which consequently dampens the

oscillation [13].

Previous experimental work by Kang and Kyritsis [14, 15] studied the propagation of methane

flames through a channel filled with a quiescent methane-air mixture with a steady, gentle gradient of

composition, which was established via a convective-diffusive balance of two distinct mixtures. Acetone

planar laser induced fluorescence (PLIF) was used to obtain real-time species concentration data, and

high-speed imaging was used to compute the flame speed. Results for methane flames propagating from

mixtures of stoichiometric composition into regions which were fuel-lean showed a substantial extension

of the lean flammability limit from a theoretical equivalence ratio of φ=0.58 to an observed minimum of

φ=0.4. Additionally, flames near the lean flammability limit were observed to propagate at speeds

significantly higher than the laminar flame speed at the local equivalence ratio. A theoretical argument in

support of this phenomenon was made using the principle of back-supported flames, which are flames

whose products are nearer to the stoichiometric composition than the reactants. A back-supported flame

can propagate from a region of rich or stoichiometric composition to one that is substantially leaner than

the theoretical flammability limit due to heat flux provided from the hot burned gases in the fuel-rich

zone [16].

Computational investigation of premixed stratified methane flames in a counterflow configuration

performed by Richardson et al. showed a similar increase in the flame propagation rate for back-

supported rich flames, and front-supported lean flames. Evaluation of species concentrations using a

detailed kinetic model indicated that for lean mixtures, the primary mechanism of flame acceleration was

a compositional-gradient induced increase in radical production, in contrast to the heat-flux based

mechanism which was observed for rich mixtures [17].

5

1.3 Combustion Instabilities

Combustion instabilities have been a topic of continued study, due to their potential to significantly

improve or degrade practical combustion performance. In premixed spark-ignition engines, the

development of flame front instability has been observed experimentally to inhibit steady-state engine

operation. This increase in cycle-to-cycle combustion variation can degrade fuel economy and increase

emissions of undesirable pollutants [18]. In premixed gas-turbine combustors, the effects of flame front

instability can be even more severe than degraded performance. Certain oscillating instabilities can

develop in turbine combustors which interact acoustically with the turbine structure. These periodic

instabilities, if they are of sufficient amplitude, can have such severe resonant effects as to physically

damage the turbine [19].

In premixed combustion, two primary modes of instability dominate: the hydrodynamic, or

Darrieus-Landau instability, and the diffusive-thermal instability. These phenomena have been studied

extensively, and a comprehensive, detailed review of them has been written by Matalon [20]. In classical

Darrieus-Landau theory, the flame reaction sheet is treated as a hydrodynamic discontinuity, the behavior

of which is determined entirely by the change in state between the burned and unburned gases.

Linearizing the fluid dynamic equations of the flame in the context of Darrieus-Landau theory yields the

following expression for the growth rate of the instability resulting from a small perturbation:

Eq. 1.1

SL is the laminar flame speed for a premixed deflagration at the specified equivalence ratio, k is the

transverse wave number of the perturbation, and ωDL is the growth rate of the Darrieus-Landau instability.

The physical implication of the instability growth rate is to indicate cases in which the flame can damp

out small perturbations, versus cases in which the perturbations will be amplified. In this formulation,

situations where the growth rate is larger than zero are those in which the flame cannot compensate for

the perturbation, and consequently destabilizes. The dependence on k indicates that short-wavelength

perturbations induce an unstable wrinkle which grows more rapidly than long-wavelength ones.

The growth rate of the Darrieus-Landau instability, ωDL, can be expressed solely as a function of the

flame thermal expansion parameter σ, which is the unburned-burned gas density ratio.

√

Eq 1.2

If a flame is present, the involved chemical reactions are exothermic, and the burned gases will be

heated and thus expanded relative to the unburned gases. This expansion necessitates that σ be greater

6

than unity, and from Eq. 1.1, it can be determined that ω will also be greater than unity. This indicates

that all premixed flames are inherently unstable in the hydrodynamic mode. It is also noteworthy that the

linear dependence on k is not preserved for perturbations which are on the order of or smaller than the

flame thickness, because the Darrieus-Landau approximation considers a flame which is infinitely thin.

If hydrodynamics was the only factor influencing flame dynamics, then it would not be possible to

create a stable planar premixed flame. These types of flames have been observed to exist experimentally,

and can be stabilized due to diffusive-thermal effects. The development of the diffusive-thermal

instability is a function primarily of the flame Lewis number, which is the ratio of the unburned gas

thermal diffusivity to the limiting-reactant mass diffusivity.

When the Lewis number is smaller than one, a small perturbation of the flame front into the

unburned region can trigger destabilization of the entire flame. Because the thermal diffusivity of the

unburned gas in these cases is low, the local flame temperature surrounding the perturbation will begin to

increase as heat is generated faster than it can be dissipated. The large mass diffusivity of the reactants in

the unburned gas continues to feed the intensifying reaction at an elevated rate, causing the perturbation

to grow, eventually disrupting the flame sheet. Consequently, flames with effective Lewis numbers of less

than unity are unconditionally unstable in this mode. In contrast, flames with large Lewis numbers are

robust against local perturbations, as the diffusive imbalance causes the perturbation to retreat back to its

original planar location. For flames with substantially large effective Lewis numbers, this diffusive

imbalance is large enough to stabilize the local hydrodynamic deformation, which allows for the

development of a stable planar flame.

The development of flame front instabilities does not exclusively lead to flame extinction.

Simulations performed of hydrogen-oxygen flames in small semi-open channels showed that the onset of

the Darrieus-Landau instability could lead to an increase in the flame propagation speed. The onset of

instability was controllable by altering the composition of the fuel-air mixture in the channel, and flame

front accelerations large enough to initiate the deflagration-to-detonation transition in the flame were

observed [21].

In addition to dependence on the flame effective Lewis number, thermal stabilization of flames can

depend on a number of environmental factors. In the case of micro-scale combustion, the physical

dimensions and thermal conductivity of the burner structure have been observed to control flame stability,

as heat losses to the burner walls become significant for small flames [22]. In a study of methane flames

in mesoscale u-shaped ducts, heat transfer between the flame and the duct walls was attributed to the

development of a stable oscillation of flame propagation, extinction, and reignition [23, 24].

7

Because the flames studied in this work are lifted flames, thermal stabilization resulting from heat

transfer to the burner will not dominate, as it does in ducted flames. The gradients of composition which

are imposed on the flame increase the diffusive flux between the fuel-rich and fuel-lean zones, which

could affect the flame stability in a positive or negative manner. If the effect of this increased diffusion is

stabilizing, then the stratified flames could be more robust against hydrodynamic perturbations.

1.4 Motivation for the Thesis

Aside from edge flames, the structure and morphology of steady stratified flames has not been

thoroughly investigated. Previous studies have been limited in focus, and have primarily been concerned

with determining the effects of stratification on flame speed and flammability limits. In this work, we

seek to provide a more fundamental description of flame behavior in stratified mixtures, and to develop

guidelines for accurate simulation of these flames.

The burner configuration presented in the immediately following section allows for study of

flame response to compositional gradients similar to those of [13], with the notable difference being that

they are established spatially instead of temporally. The flames propagate in a controlled, steady

distribution of mixture composition, which varies significantly at short length scales. This allows the

flame response to be observed at a steady state, which can also allow for further investigation into the

transient heat-flux stabilization effects suggested by previous work.

This work will present both preliminary experimental and computational data regarding the

behavior of these stratified flames. Chemiluminescence imaging was used to visualize the flame reaction

zone in the laboratory, and an initial attempt to recreate this behavior has been made using a planar

numerical model. The effects of kinetic model reduction are considered in light of initial computations

predicting the formation of a flame instability which was not observed experimentally, as well as the

influence of various intermediate and radical species. Computational results are compared qualitatively

with the experimental images in terms of basic flame structure as well as radical emission intensity.

Comparison between the computations is performed on the basis of flame liftoff, temperature, and local

mixture composition. Analysis of stretch imposed on the flame front by the compositional gradients is

also considered as a mechanism of the observed flame wrinkling.

8

Chapter 2: Apparatus and Computational Model

2.1 Parallel Flame Stratification

In contrast to the widely-studied edge-flames, where compositional stratification develops

perpendicularly to the direction of flame propagation, the configuration of interest in this study was a

periodic composition of gradient parallel to the flame propagation. A conceptual diagram of this flame

configuration is provided in Figure 2.1.

As shown in the figure, the flame structure of interest is established by introducing two distinct

air-fuel mixtures in an alternating pattern, one of which is relatively rich, denoted φR, and the other

relatively lean, denoted φL. The laminar flame speed, and thus the overall flame propagation rate in each

localized region, is directly correlated to the mixture composition. Flames propagate at the highest rate

when the air-fuel mixture is in the stoichiometric ratio, that is, when the equivalence ratio, φ, is equal to 1.

Thus the introduction of two different mixtures will create a flame front which is wrinkled in structure, as

shown, due to the different local flame speeds. The flame depicted shows a case where both mixtures are

overall rich, thus the leaner mixture is nearer to the stoichiometric ratio, so the flame speed is higher, and

the liftoff distance is shorter.

Figure 2.1. Establishment of a parallel gradient of mixture composition.

9

In this configuration, it is possible to control a number of parameters which can impact the

structure of the stratified flame. These parameters account for both the effects of chemistry and mixing as

well as flow hydrodynamics. It is possible to vary the overall mean equivalence ratio of the mixture,

allowing for comparison between cases in which the flame is in the overall lean or rich regions, or when

the stratification occurs across the stoichiometric ratio. For simplicity, this parameter will be defined as

the approximate mean equivalence ratio:

Eq. 2.1

Because both the flow rates of fuel and oxidizer are varied in this study, the true mean equivalence ratio

of the mixture is not exactly equal to this expression. The variations in air flow rate in the most extreme

cases of stratification observed were less than 4% between the rich and lean flows, so the actual mean

equivalence ratio will not deviate largely from the approximate value. This formulation allows for a more

convenient comparison of flames in varying conditions.

In addition to the mean equivalence ratio, it is also possible to vary the increment of

compositional stratification, which is defined as:

Eq. 2.2

ΦS is thus an indicator of the strength of the stratification. A small value of φs indicates two mixtures of

very similar composition, whereas a larger value of φs indicates highly dissimilar mixtures.

In order to control the spatial gradient of equivalence ratio, the characteristic length of

stratification, which will also be referred to as the stratification length, L, is also a relevant experimental

parameter. Preserving the same increment of stratification, φs, and decreasing the stratification length

steepens the compositional gradient, and extending the stratification length has the opposite effect. As

shown in the figure, the stratification length is defined as the width of a single inlet to the stratified

burner. In each individual test case, the inlet width was kept constant for all of the burner inlets. For

practical purposes, the stratification length was slightly larger than the actual inlet size, because dividing

walls of small thickness were required between the slots to separate the flow streams.

Because it is intended that the flame remain stationary with respect to the burner surface, the

velocity of the upstream air-fuel mixture, V, also controls the behavior of the stratified flame. As the

overall equivalence ratio is moved further from stoichiometry, the global flame speed will be reduced,

increasing the likelihood that the flame will blow off and extinguish at higher upstream speeds.

Conversely, a more rapidly propagating flame can flash back and extinguish in flow fields with smaller

10

speeds. Between these two limiting conditions exists a range of flow rates in which the stratified flame

can stabilize at varying liftoff heights and flame structures.

2.2 Experimental Flame Imaging

2.2.1 Micro-Slot Burner

In order to facilitate the establishment of a periodic modulation of the local equivalence ratio, a

specially-designed, micro-fabricated 13-slot burner was utilized. This apparatus allowed two distinct air-

fuel premixtures to be introduced to the flame reaction zone at a small length scale. The structure of the

burner is comprised of a machined aluminum cube, with 13 slots of width 0.8 mm and height 1.0 cm,

spaced 0.2 mm apart, cut from the top to the bottom surface of the burner. The bottom face of the burner

is sealed with a plastic film to ensure that the incoming mixture exits from the upper slot openings. Figure

2.2 shows a top-view photograph of the slotted burner.

To ensure better flow alignment and reduce divergence at the slot exits, stainless steel meshes of

0.0022 in wire diameter and 30% overall open area were inserted into the top of each slot, and were

secured using a high-temperature sodium-silicate gasket cement. The two brass fittings shown are the

inlets through which the two selected air-fuel mixtures are introduced. The gas flowing through one of

these inlets passes first into one of two open cavities on either side of the burner. The side chambers are

exposed to facilitate modification of the slot flow configuration, and are sealed during use with plastic

film. A schematic diagram of the burner side cavity is provided in Figure 2.3.

Figure 2.2. Top view of micro-slot burner.

11

Figure 2.3. Side view of micro-slot burner.

Within each of the side cavities, which are identical, there are 13 holes bored in the burner wall,

which correspond to the 13 burner slots. These holes are bored through the full width of the burner,

passing from one side cavity, through a single burner slot, and then finally into the opposite side cavity.

This configuration allows the selection of target slots for inlet gas from either cavity to be controlled

simply by selectively exposing or covering the holes on either side. In the configuration shown, the holes

are covered and exposed in an alternating pattern on the visible side, and vice-versa on the opposite side,

creating a characteristic length of stratification of 1-slot width, or 1 mm when including the slot spacing.

Additionally, a quartz glass chimney of a diameter significantly larger than the flame size was placed over

the top of the burner to isolate the flame from ambient air currents in the room which could destabilize the

structure.

2.2.2 Mixture Flow Control

Control of the incoming mixture equivalence ratio was achieved by metering the inlet air and

pure fuel on a volumetric basis. For each mixture, the air and fuel were metered individually,

corresponding to the proper volume fractions, and were mixed substantially far upstream of the burner

inlet to ensure homogeneity. Air flows were controlled using Omega model FL-3839G-HRV rotameters,

which were calibrated using air at 21° C and 1 atm metering pressure. Flow measurements on the

rotameters are presented in arbitrary units, on a scale of mm of tube height. It was possible to determine

the rotameter float position to an accuracy of approximately 0.5 mm on the scale, which corresponds to

12 sccm for air at atmospheric pressure. For the air flow rates considered in this study, the measurement

error in volumetric flow rate of air introduced by the rotameter scaling amounted to 2-3%.

12

Figure 2.4. Schematic diagram of flame imaging.

As is usual for combustion with air as the oxidizer, the required flowrates of fuel were

substantially lower than those of air. To ensure precise metering, mass flow controllers were used for the

fuel streams. In cases where propane fuel was used, the flow was controlled using Omega mass flow

controllers with capacity 0-200 sccm N2. Due to its lower stoichiometric air/fuel ratio, methane required

flowrates exceeding the upper limit of the Omega controllers. For the methane fuel cases, MKS mass flow

controllers with capacity 0-5 slpm N2 were used.

2.2.3 Optical Setup

Because the flames observed in this study were generally rich, visibility of the reaction zone was

obscured by luminous soot emission downstream of the flame sheet. In order to visualize features of the

reaction sheet, the natural chemiluminescence of the OH* radical was utilized. A strong OH* emission in

flame reactions occurs due to an electronic transition from the A 2Σ

+ excited state to the X

2Π gr u

state, which emits at 306 nm [25]. To isolate the OH* emission, an Edmund Optics band-pass interference

filter centered at 310 nm with a FHWM bandwidth of 10 nm was utilized. For most hydrocarbon flames,

CH* radical emission also contributes to the natural chemiluminescence, with the strongest emission

bands at 431 and 390 nm. There is a CH* emission corresponding to 314 nm, but it is weak in comparison

to the OH* in the pass band of the filter used [26].

As shown in Figure 2.4, images were captured using an Andor technologies iStar intensified CCD

camera, fitted with a UKA optics UV8040BK quartz ultraviolet lens (f/3.8) to eliminate distortion of the

13

Figure 2.5. Schematic diagram 2D computational domain.

image. The images were taken with a CCD gain of 0, gate width of 5 ms, re ut time f 16 μs. F se

coloring was then added to the images using the Andor Solis software to indicate the relative intensity of

the emission.

2.3 Computational Model

2.3.1 Domain and Boundary Conditions

To keep the computational cost, and thus the required time of simulation at acceptable levels, the

micro-slot burner was modeled in two dimensions using a planar cross-section of the inlet slots. A

diagram of the planar domain is provided in Figure 2.5.

The rectangular domain encloses the region immediately above the surface of the burner, up to a

height of 5.5 mm, which was able to capture the relevant flame structure. The width of the domain is

14.48 mm, featuring side walls situated slightly beyond the edge of the outermost inlets. The region of the

burner below the outlet surface was not considered relevant to the flame behavior, since no combustion or

interaction between the two incoming mixtures occurs within the burner itself. The domain was meshed

using quadrilateral grid elements of uniform 0.1mm x 0.1 mm dimension. This resolution was able to

sufficiently capture the flame structure in the reaction zone without adding the computation time

associated with local grid refinement.

14

The mixture inlets were modeled using a velocity-inlet boundary, in which the flow velocity was

kept at a constant value and assumed to be purely one-dimensional, in the direction normal to the burner

surface. This assumption was made considering that the inlet flow channels were sufficiently long for the

flow to become fully developed before reaching the top of the slot, and that the meshes inserted into the

slot outlets approximately aligned the flow. To confirm the assumption of fully developed flow, a simple

entrance length calculation was performed [27]. For laminar flow, the required entrance length for the

flow to become fully developed is approximated as:

Eq. 2.3

where Dh is the hydraulic diameter of the slot and Reh is the Reynolds Number for a non-circular pipe

flow. Approximating the incoming mixture as air at 298 K, the Reynolds Numbers of this flow ranged

between 60 and 80, with a maximum entrance length of 7.5 mm, which is substantially shorter than the

length of the slot.

The temperature of the incoming gas was assumed constant at an ambient temperature of 300 K,

and the equivalence ratio of each mixture was controlled using explicit mass fractions of fuel and oxygen.

It was assumed for the modeling of species concentrations that any remaining mass fraction of the

mixture not explicitly defined was occupied by nitrogen.

The base of the burner was modeled as a solid aluminum wall, and material properties were taken

from the materials database of the solver software, described in detail in the next section. The inset of

Figure 2.5 shows that each of the inlet slots was subdivided into three smaller inlets by thin solid walls.

These subdividing walls simulate the steel meshes inserted into the experimental burner, and each have a

width which is equal to the nominal mesh wire diameter. For practical purposes, these dividers were

modeled with the same conditions as the rest of the burner base. A no-slip momentum condition was

applied at the burner base, and constant temperature was fixed at 450 K. This elevated temperature was

chosen to approximate the heating of the burner surface from the flame stabilized a small distance above

it.

The side walls of the computational domain were significantly closer to the flame zone than the

glass walls of the chimney used in the experiments, however for computation cost purposes it was

desirable to keep the area of the domain to a minimum. Because of this, the walls were modeled with

boundary conditions intended to reflect the properties of ambient quiescent air trapped within the

surrounding chimney. As such, a zero-shear boundary condition was imposed, because a no-slip condition

15

would be inappropriate here. Additionally, the walls were treated as adiabatic, modeling the low thermal

conductivity of quiescent air.

The outlet plane of the domain was modeled with an outlet pressure condition imposed at

atmospheric pressure. The outlet temperature was assumed to be constant at 300 K ambient temperature,

and the species composition in the outlet region was imposed as standard air, composed of 21% oxygen

and 79% nitrogen by mass.

2.3.2 Solver Configuration and Initial Conditions

Flame calculations were performed using the commercially-available ANSYS FLUENT 12.1

computational fluid dynamics software package. FLUENT is a comprehensive software tool capable of

simulating laminar or turbulent flows, in single or multiphase configurations by solving for continuity and

conservation of momentum. The code can also solve the energy conservation equations, which it then

uses to compute heat transfer and effects of chemically reacting flows. For reacting systems, species and

reaction data can be computed using either an integrated chemistry solver or with an optional CHEMKIN

plug-in which provides extended functionality.

The FLUENT pressure-based solver was used to perform the calculations in this study. For the

reduced chemistry calculations, the default solver parameters were used for pressure, energy, momentum,

and all relevant species. In the cases where detailed chemistry was used in the computation, second-order

spatial discretization for pressure was utilized. The transient solver was used, with a uniform time step of

1x10-5

s, which was sufficiently small to ensure convergence without requiring an excessive number of

iterations. The initial calculations using reduced chemistry were solved for 3850 time steps to ensure that

the solution was not influenced by transient effects resulting from ignition. Using the detailed models, it

was found that 2500 time steps was sufficient to eliminate ignition effects without adding unnecessary

computation time. The iteration limit for each time step was set to 400, and the under-relaxation factors

used to determine convergence were left at their default values in all cases.

The laminar viscous flow model was selected, as turbulent flames were not considered in this

study. The energy equation model as well as species transport were enabled, including volumetric

reactions and diffusion energy sources. Enabling the thermal diffusion model had a negligible effect on

the final result while adding substantially to the computation time

In the cases using reduced chemistry, the full multicomponent diffusion model did not have a

noticeable impact on the results due to the relatively low number of species considered, and mixture-

averaged diffusion was used instead. Mixture density was computed using the incompressible ideal gas

16

law, and specific heat was computed using the dilute mixing law. Mixture viscosity was assumed constant

and the thermal conductivity was computed using a piecewise polynomial fit. Mass diffusivities were

computed by the code using kinetic theory.

For the detailed chemistry cases, mixture density was again computed using the incompressible

ideal gas law. Species diffusion and all other relevant transport properties were computed using the

CHEMKIN-CFD solver package and transport property databases for each specific mechanism, excluding

the mechanism for n-heptane, which did not include a transport properties file; in this case the same

methods were used as the reduced chemistry cases.

In all of the tested cases, the computational domain was initially filled with quiescent air of

composition 21% oxygen and 79% nitrogen by mass, at a temperature of 2000 K. This elevated

temperature was used to facilitate the ignition of the incoming fuel without necessitating the use of a

spark, and because the outlet condition was maintained at ambient temperature, the amount of time

required for the domain temperature to reach a steady-state was negligible. Thermal radiation effects were

not accounted for in this model.

2.3.3 Reduced Kinetic Mechanisms

Computations involving reduced chemistry were performed using the FLUENT stiff-chemistry

solver and built-in reaction mechanisms for propane, methane, and n-heptane in air. The FLUENT

database chemistry mechanisms are based on global 1 and 2-step reaction models, using laminar, finite-

rate chemistry, and ignore backward reactions unless explicitly specified. Reactions are modeled using

individual Arrhenius equations with forward-reaction rate constants of the form:

(

) Eq. 2.4

Ar is the pre-exponential factor, βr is the temperature exponent, and Er is the activation energy of the

reaction. These parameters, along with stoichiometric coefficients, are unique to each individual reaction

and are computed from the materials property database. R is the universal gas constant. Further details on

the FLUENT chemistry solver are available [28].

17

Propane flame calculations were performed using the Propane-Air-2Step mechanism, a 5-species

model built on 2 global reaction steps, and using the following 3 elementary reactions:

Eqs. 2.5

Methane flames were computed using the similarly structured Methane-Air-2Step Mechanism, again

comprised of 5 reacting species and 3 elementary reactions:

Eqs. 2.6

In these 2-step reaction mechanisms, the only intermediate species considered was carbon

monoxide, which is a significant caveat of these models. According to Law [29], the two primary

reactions in hydrocarbon oxidation are:

Eqs. 2.7

This implies that the primary pathway for carbon monoxide oxidation is actually through a reaction with

the hydroxyl radical, as opposed to oxygen, as modeled in the 2-step mechanisms. The generation of the

hydroxyl radical requires the presence of atomic hydrogen, which is typically produced as a significant

intermediate along with carbon monoxide in rich combustion. Because these models do not account for

atomic hydrogen, they neglect this important branch of the oxidation mechanism.

For the n-heptane reactions, even the carbon monoxide oxidation step was neglected in the

mechanism, leaving only a single elementary fuel oxidation reaction (N-Heptane-Air).

Eq. 2.8

2.3.4 Detailed Kinetic Mechanisms

The detailed reaction chemistry was computed using the commercial CHEMKIN-CFD software

package, a plugin designed to integrate with the FLUENT flow solver environment. Due to the high

18

computational cost involved in adding additional species to the conservation equations, the FLUENT

solver limits all reaction mechanisms to a maximum of 50 reacting species, although it places no explicit

limit on the number of elementary reactions. Considering this point, it is to be noted that the detailed

mechanisms employed in this study are not full kinetic models. The mechanisms chosen have been

reduced via a number of different techniques, but can nonetheless more accurately reflect full flame

chemistry than a one or two-step global reaction model.

For propane combustion, the Propane_NOx_HighT mechanism, specially modified by Reaction

Design for use in CHEMKIN-CFD, was utilized. The model was originally derived from a

comprehensive multicomponent model intended to simulate the combustion of soy and rapeseed biodiesel

by modeling 5 of its primary constituents [30]. Using Reaction Workbench software, the mechanism was

reduced first by removing all of the species and reactions unrelated to propane combustion, and then

corrected to conditions of a slightly-lean, elevated pressure, laminar propane-air flame using the direct-

relational graph method [31]. The resulting mechanism is comprised of 37 reacting species and 211

elementary reactions. This mechanism, as well as the others used in this work, is provided in Appendix A.

To compute methane flames, the Grimech30_50spec mechanism provided by Reaction Design

was used. The model is nearly identical to the stock GRI mechanism intended to model the combustion of

natural gas, except that it has been reduced from 53 reacting species to 50 in order to comply with the

limits imposed by FLUENT. The eliminated species are propane, the propyl radical, and argon. The

skeletal propane combustion model is included in the standard GRI mechanism because natural gas

generally contains significant quantities of propane. Because this mechanism has been intended to model

the combustion of pure methane, the propane component was discarded. The GRI mechanism is well

established and its authors have collected extensive validation data for criteria such as ignition delays,

laminar flame speeds, and species profiles [32]. After the reduction, the final mechanism is composed of

50 reacting species and 308 elementary reactions.

Because mechanism size grows rapidly with the complexity of the hydrocarbon fuel molecule, the

mechanism selected for n-heptane combustion was a further reduction of a previously-developed skeletal

mechanism [33]. Detailed mechanisms for n-heptane are large, such as the mechanism of Curran et al.,

which includes 570 reacting species and 2520 elementary reactions [34]. To enable coupling with a CFD

model, a skeletal heptane mechanism was developed by Golovitchev, which reduced the model to 40

species and 165 reactions [33]. Using a genetic algorithm, this model was further reduced to 29 species

and 52 reactions, with ignition delay and temperature profile validation provided in conditions similar to

HCCI engine operation [35].

19

Chapter 3: Experimental and Computational Results

3.1 Stratified Flame Structure

3.1.1 Radical Natural Chemiluminescence Imaging

Both methane and propane flames were visualized using the burner and optical configuration

described in Chapter 2. The flame wrinkling effect of interest in this study was more pronounced as the

overall equivalence ratio was increased to richer than stoichiometric. A mean ratio of 1.4 was selected for

the initial propane experiments because it allowed for the variation of φS up to a value of 0.6 without

including a stoichiometric crossing, which could have effects on the flame front in addition to those of the

compositional gradient. Propane flames were also imaged at a mean equivalence ratio of 1.7 to view the

effects of further enrichment. For the methane flames, it was unavoidable to cross the stoichiometric point

if the same degree of stratification was to be achieved as for propane. This is due to the fact that the rich

flammability limit for methane in air, φ=1.6, is substantially lower than that for propane, φ=2.5 [36].

Consequently, using the same mean equivalence ratio of 1.4 selected for propane would exceed the

flammability limit for cases where φS>0.4, leading to extinction effects which would obscure observation

of the stratification effects.

For each mean equivalence ratio condition, the flames were observed under 32 different operating

configurations. Four upstream flow velocities were considered: V= 65 cm/s, 70 cm/s, 75 cm/s , and

Figure 3.1. Spatial gradients of composition

20

80 cm/s. At each velocity, the flame stratification, φS was increased from 0 (uniform composition) to 0.6

in increments of 0.2. Additionally, the flames were observed at two characteristic lengths of stratification:

L=1 mm and 2 mm. Figure 3.1 shows the variation of the spatial gradient of composition at L=1 mm as a

function of the increment of stratification for the three mean equivalence ratios considered, as well as for

n-heptane flames at φ=1.4, which are included only in the computational portion of this work. Because

the gradient varies linearly with the stratification length, the L=2 mm cases would show the same trend,

with magnitudes reduced by a factor of 2. It can be seen that the gradients imposed on the flames are

comparable for all of the fuel conditions selected.

Figure 3.2 shows the visualized chemiluminescence for propane-air flames at a mean equivalence

ratio of 1.4 for values of φS up to 0.2.

In Figure 3.2a, the flame shows a nearly planar structure, which is expected in the case where the

mixture and upstream flow conditions are uniform. Some very slight wrinkling is present, but this is

likely the result of discontinuities in the flow field resulting from the dividers placed between the burner

slots. The slight smearing in the image seen in the 70 cm/s and 75 cm/s case is the result of noise in the

CCD signal. Efforts were made to minimize the visibility of this noise by adjusting the scaling of the

coloration, but when the emitted intensity was low, any further adjustment resulted in portions of the

flame sheet becoming no longer visible. The relative intensity of emission is approximately constant, with

lower rates of reaction in positions corresponding to the slot dividers. There is a single region slightly to

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

a) φS=0, L=1 mm b) φS=0, L=2 mm c)φS=0.2, L=1 mm d) φS=0.2, L=2 mm

Figure 3.2. Propane flames at an average φ=1.4

21

the right of the center slot in which the emitted intensity is consistently low, which is also visible in

Figure 3.2c, with an approximately corresponding location of peak emission for the 2 mm stratification

length cases shown in Figures 3.2b and d. This phenomenon appears to be a consequence of the data

collection technique and bears no apparent effect on the flame behavior.

Extending the stratification length for the homogeneous case shows similar flame structure, an

approximately planar flame with approximately constant chemiluminescence signal. The light wrinkling

visible here with a wavelength corresponding to the stratification length is most likely caused by a slight

variation in flow velocity between the two mixtures within the control accuracy range of the instruments

used. Application of a mild compositional stratification, as shown in Figures 3.2c and d, has a nearly

negligible effect on the overall flame structure. There is a slight decrease in the amplitude of the wrinkle

in the L=2 mm case as the upstream velocity is increased, but again it is small enough that this may just

be the result of flow control. The cases where the compositional stratification was more severe are shown

in Figure 3.3.

In Figures 3.3a and c, where the stratification length was 1 mm, the formation of a wrinkled flame

surface becomes just barely visible as the compositional gradient becomes large. The structure of the

wrinkled flame is as expected, in that the wavelength of the wrinkle corresponds to that of the periodic

gradient of composition, and two stable liftoff heights are established, which are consistent among the

slots of equal composition. It is also possible to see that an alternating pattern in the emission strength has

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

a) φS=0.4, L=1 mm b) φS=0.4, L=2 mm c)φS=0.6, L=1 mm d) φS=0.6, L=2 mm

Figure 3.3. Propane flames at an average φ=1.4

22

begun to form, and the peak intensities roughly correspond with the flame regions which have the largest

local curvature.

The increased amplitude of flame front wrinkling is even more visible in the L=2 mm cases

shown in Figures 3.3b and d. Again the period of the wrinkle corresponds to the period of the equivalence

ratio modulation. It is difficult to discern whether these flames exhibited the same alternating pattern of

peak emission intensity, as the scaling is skewed by the single region of high intensity which has been

described previously. It can also be seen in both cases at L=2 mm that the amplitude of the flame front

wrinkle decreases with a corresponding increase in the upstream flow speed, which suggests that at higher

propagation speeds some of the diffusive effects are damped by hydrodynamics.

Figure 3.4 shows images of methane flames taken at a mean equivalence ratio of φ=0.9, with

stratification up to φS=0.2.

An immediately notable feature of these images is the fact that the luminous zone of the flame is

not as clearly defined as for the propane flames. The emitted intensity of the methane reaction was lower

than for propane, and, as a result, the signal-to-noise ratio was less favorable, resulting in images which

appear somewhat blurred, which is likely due in part to the lower levels of soot produced by methane

flames, leading to lower overall flame luminosity. Nonetheless, the defining features of these flames are

similar to the propane flames at low degrees of stratification. The flames appear nearly planar, with some

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

a) φS=0, L=1 mm b) φS=0, L=2 mm c)φS=0.2, L=1 mm d) φS=0.2, L=2 mm

Figure 3.4. Methane flames at an average φ=0.9

23

very small amplitude wrinkling, which is a result of flow field perturbation, and in the homogeneous case

the reaction rate is approximately evenly distributed. At slight stratification the alternating pattern in

reaction rate which was observed for the propane flames begins to become evident. In the L=2 mm cases

(Figures 3.4b and d) there is a visible discontinuity in the radical emission, however this is attributed

again to the imaging process, as direct observation of the natural luminescence of the flame during

experiments showed an unbroken flame front. The effects on flame structure as the stratification was

increased up to φS=0.6 are shown in Figure 3.5.

As with the cases with lower stratification increments, the low emission intensity of the methane-

air flames resulted in noise-related blurring of the captured images. Again the amplitude of the flame-

front wrinkle increases slightly with corresponding increases in stratification, which is reasonable

considering that the individual laminar flame speeds of each mixture become increasingly dissimilar. It

should also be noted that because the methane flames are centered about an equivalence ratio of 0.9,

which is overall lean, as pp se t the pr p e f mes which were ver rich, the “tr ughs” f the

flame wrinkle, or those regions closest to the burner surface, correspond in this case to the locally rich

mixture. At φS=0.6, the rich mixture has an equivalence ratio of 1.2, as opposed to 0.6 for the lean

mixture, and thus the richer flame will propagate nearer to the stoichiometric flame speed. It can be

observed in these flames, particularly those in Figures 3.5b and d, that an alternating pattern of emission

intensity also develops in the methane flames. The locations of peak emission correspond to the troughs

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

a) φS=0.4, L=1 mm b) φS=0.4, L=2 mm c)φS=0.6, L=1 mm d) φS=0.6, L=2 mm

Figure 3.5. Methane flames at an average φ=0.9

24

of the wrinkle, where the flame composition is nearest to the stoichiometric ratio, and thus the local rate

of reaction is maximum.

Direct observation of the flames during the experiments suggested that the formation of the

wrinkled structure became more pronounced as the overall mixture was enriched. While methane

presented a limiting case due to its low rich flammability limit, propane offered freedom to explore the

effects of stratification on increasingly rich flames. Figure 3.7 shows the flame reaction zones for propane

air mixtures at φ=1.7 in both the homogenous case and at a stratification increment of φS=0.2. The V=85

cm/s cases are not provided for Figures 3.6a and b because the fuel flowrate required was in excess of that

which could be delivered by the equipment used.

These flames have a number of defining features which clearly separate them from the leaner

propane flames shown in Figures 3.2 and 3.3. In the L=1 mm cases of Figures 3.6a and c, the overall

flame structure is nearly planar, again with a slight visible wrinkle. Unlike in the previous cases however,

this wrinkle cannot be attributed to variation in flow velocities between the two inlet mixtures, because

the wavelength of the disturbance does not correspond with that of the mixture modulation. This effect is

most visible in the cases where the inlet velocity was low, and as shown in Figure 3.6c, seems to be

mitigated by elevated flowrates. In fact, the reaction zone at 85 cm/s in Figure 3.6c is nearly identical to

that of the corresponding leaner flame in Figure 3.2c.

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

a) φS=0, L=1 mm b) φS=0, L=2 mm c)φS=0.2, L=1 mm d) φS=0.2, L=2 mm

Figure 3.6. Propane flames at an average φ=1.7

25

Increase of the stratification length to L=2 mm, as shown in Figures 3.6b and d, produced even

more drastic effects on the flame structure, as well as a possible explanation for this behavior. Figure 3.3b

displays the case of the homogeneous mixture flame. The reaction zone was not, however, observed to be

planar in any of the three flowrate cases selected. At the lowest mixture flowrate of 65 cm/s, it is nearly

impossible to distinguish the boundaries of the reaction sheet. Instead, the widely distributed reacting

region and roughly plume-shaped flame indicates a mode of combustion which is nearer to a diffusion

flame than a premixed deflagration. As the flow velocity is increased to 70 cm/s, the region of peak

radical emission becomes more visible and begins to flatten, although there is still a substantial region

downstream where the products of incomplete rich combustion continue to react. As shown in Figure

3.6d, at 85 cm/s, the flame reaction zone becomes nearly planar when the flow velocity is sufficiently

high, although the flame thickness is clearly larger than for the corresponding leaner flames. One possible

explanation for this flattening effect is that at higher flow rates, the products of incomplete combustion

are carried sufficiently far downstream into the lower temperature burned gases before they are able to

react. It is also interesting to note in Figure 3.5c that at V=75 cm/s, the intermediate structure of the

flattening flame is a roughly sinusoidal wrinkle which strongly resembles the stratification-induced

wrinkles, despite that fact that the mixture is uniform. Additionally, when the stratification length is

reduced to L=1 mm, the plume structure to planar reaction transition is not observed over the same range

of mixture flowrates, which could suggest that the larger compositional gradients in this configuration

affect the local reaction rate of the flames. These enriched flames are shown for cases up to a

compositional stratification of φS=0.6 in Figure 3.7.

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

a) φS=0.4, L=1 mm b) φS=0.4, L=2 mm c)φS=0.6, L=1 mm d) φS=0.6, L=2 mm

Figure 3.7. Propane flames at an average φ=1.7

26

The first notable characteristic of these flames is that in general, increasing the compositional

stratification tended to drive the flame structure toward a wrinkle more closely resembling that of the

leaner flame. In the L=2 mm cases of Figures 3.7b and d, the wrinkled structure of equal wavelength to

the mixture modulation is clearly visible, particularly at higher flow speeds. At the lowest speed, the

flames still show some characteristics of diffusion combustion, but the beginnings of a planar reaction

zone are more readily visible than when the stratification was low in Figure 3.6. The alternating pattern of

emission is again visible for these flames, with the peak intensities corresponding to the troughs of the

wrinkled structure. For L=1 mm in Figures 3.7a and c, the tendency for the flame wrinkling to reduce in

amplitude and wavelength with increasing flow speed was also observed, except for the anomalous case

of φS=0.4, which seems to be an experimental error given that its behavior lies far outside the trend of

similarly configured flames.

Reviewing all of the flames, some general trends in behavior were observed. In all of the cases,

the flames were stabilized in an approximately planar configuration when the stratification was zero and

the overall mixture was not excessively rich, and increases in the compositional gradient caused the

development and corresponding increase in amplitude of a wrinkled flame structure. Depending on the

severity of the stratification, this wrinkling could be either partially or completely damped out by

increases in the incoming mixture flow speed. This effect was most noticeable for flames which were

overall very rich, which transitioned from plume-shaped flame to nearly planar at higher speeds. Once

this wrinkling developed, there were clearly identifiable maxima in the radical emission, corresponding to

maxima of local reaction rate, in the regions of the flame that were closest to the burner surface, which

had compositions nearest the stoichiometric ratio.

3.1.2 Flame Simulation with Reduced Chemistry

The first iteration of the computational models developed to predict stratified flame behavior

utilized the heavily reduced global reaction mechanisms are outlined in Chapter 2. These were selected

both for simplicity of implementation as well as low relative computational cost. A first step toward

validation of these models using the imaging data gathered in experiments was to compare the structure of

the computed flame reaction zones for qualitative agreement. The nature of the reduced mechanisms,

however, prevented an exact comparison between the two. As detailed in Equations 2.5, 2.6, and 2.8, the

reduced mechanisms consider only carbon monoxide as a reaction intermediate, if any intermediates are

considered at all. Because of this, the concentration profiles of the OH radical cannot be determined in the

simulated flames. Since the number of reactions computed in the reduced mechanisms is very limited, the

FLUENT chemistry solver is able to track rates of each individual reaction. In the 2-step reduced

27

mechanisms utilized for propane and methane, only the first elementary reaction includes any fuel

oxidation, while the latter two are simply the forwards and backwards reaction of carbon monoxide with

oxygen. Thus the approximate flame structure was determined for these simulations by plotting the rate of

these primary reaction steps. Because the OH* emission coincides approximately with the flame reaction

sheet, the locations of peak radical emission and peak fuel reaction can be assumed roughly coincident,

within a small error. In the case of the n-heptane flames studied in these computations, the flame structure

was determined using the rate of the only reaction step in the global mechanism. Figure 3.8 shows the

computed reaction zones after 3850 time steps for propane-air flames at φ=1.4 with a stratification length

L=1 mm.

In Figures 3.8a-d, when the upstream mixture speed was low, in this case 65 cm/s, there is a good

qualitative agreement between the predicted flame structure and the experimentally observed flames in

Figures 3.2 and 3.3. With no stratification, the flame is approximately planar, with some slight

perturbation caused by variations in the flow field created by the slot dividers. Increasing the

compositional gradients leads to the formation of an increasing-amplitude wrinkle with a wavelength

corresponding to the characteristic length of stratification. Additionally, the local rate of reaction is the

strongest in the regions of the flame closest to the burner surface.

For flow velocities in excess of 65 cm/s however, the predicted flame structure diverged

increasingly from the experimental observations. Figure 3.8a shows the effects of increased mixture

flowrate independent of stratification. Higher flow speeds cause two large deformed peaks to form in the

planar flame front, which become increasingly lifted from the burner surface. At 85 cm/s, a third

deformation peak develops in the center of the lifted region. Increasing the stratification appeared to

partially dampen the deformation triggered by an increase in the flow velocity, as shown in Figures 3.3c

and d. The flames at 70 cm/s show a deformation which resembles a superposition of the short

V=65cm/s

V=70cm/s

V=75cm/s

V=85cm/s

a) φS= 0 b) φS= 0.2 c) φS= 0.4 d) ) φS= 0.6

Figure 3.8. Propane reaction zones at φ=1.4, L=1 mm

28

wavelength wrinkle arising from stratification and the large wavelength deformation, which at φS=0.6

appear to destructively interfere, leading to a flattening of the leftmost deformation peak. In Figure 3.3c,

at 75 cm/s this interference between deformations appears to inhibit the formation of the central lifted

flame region, which is clearly visible at the lower stratification cases. At 85 cm/s, the center lifted region

develops, but only the single center peak is well defined, as opposed to the three-peaked structure. For the

maximum stratification observed in Figure 3.8d, the effect of compositional gradient is sufficiently strong

to prevent the center of the flame from lifting off at any of the flowrates tested. This result is an

interesting contrast to the experimentally observed flames, in which any observed wrinkling was most

severe at the highest gradients of composition, and the flames tended to become increasingly planar with

increased mixture flow speed.

Figure 3.9 shows the predicted flame structures when the stratification length was extended to

L=2 mm with the maximum stratification φS=0.6. What is

immediately noticeable is that the increase in stratification length

completely prevents the development of the large scale flame

deformation which was observed at high speeds in Figure 3.8.

This result is counterintuitive, in that the L=1 mm cases suggested

that the deformation was most effectively damped when the local

compositional gradients were maximum. Doubling the

stratification length however, decreases the local gradients by a

factor of 2, so it could be expected that the deformation would be

more severe in the 2 mm case. This in turn suggests that the

mechanism by which the flame front deforms may not be coupled

to the length scale of the stratification solely in terms of the compositional gradient.

As described in the introduction, the classical hydrodynamic theory used to describe flame

structure cannot predict the effect of disturbances with a wavelength on the order of or smaller than the

flame thickness. The classical flame thickness, δ, is considered to be infinitesimally small, so

perturbations cannot occur at a length scale smaller than δ. However, more realistic flame models

acknowledge the fact that the chemical reactions which occur in the flame sheet have a high activation

energy, so a preheat zone of finite thickness is required to initiate combustion. In this preheat zone,

certain components of the flame kinetics begin prior to the reaction sheet, and so a more practical

formulation of the complete flame thickness, δL, is [37]:

Eqs. 3.1

V=65cm/s

V=70cm/s

V=75cm/s

V=85cm/s

Figure 3.9. Propane reaction zones at

φ=1.4, φS=0.6, L=2 mm.

29

β is the Ze ’ vich um er, which is fu cti f the ver re cti ctiv ti e ergy EA, the

universal gas constant R, the adiabatic flame temperature Tf, and a reference temperature T0, which is

typically taken to be the unburned gas temperature. For a typical hydrocarbon flame, according to

Glassman [36], the overall activation energy can be approximated to be roughly 160 kJ/mol, and the

adiabatic flame temperature is approximately 2100 K. From these assumptions β is roughly 10 and the

flame thickness δL is about 1 mm.

Because the reduced kinetic models employed in these computations are extremely simple, the

computed flame structures depend heavily on the aerodynamics of the reaction zone. When the

characteristic length of the wrinkling caused by mixture stratification is reduced to the order of the flame

thickness, the hydrodynamic models can no longer adequately capture the flame behavior, which could

depend heavily on local kinetic effects.

Returning to the flames displayed in Figure 3.9, it can be seen clearly that, as was the case with

the experimentally observed flames, the reaction rate is maximum nearest the burner surface. The wrinkle

which develops in the computed flames is periodic, but each period of the wave is asymmetric, that is, the

trough regions are noticeably wider and flatter than the peaks, which appear to be compressed and show a

sharp curvature. It is also interesting to note that while the flame front does not destabilize, the amplitude

of the compositionally-induced wrinkle grows as the mixture flowrate increases, which is the opposite

trend seen in the experiments.

Figure 3.10 shows computed methane reaction zones

at φ=0.9, with a stratification of φS=0.6 and stratification

length of L= 1 mm. What is immediately noticeable is that

unlike the propane flames, the methane flames do not exhibit

a large scale deformation with increasing upstream flow rate,

even at a short characteristic length. In fact, the wrinkled

structure of the computed flames appears to deviate even less

from a perfect plane than the flames observed in the

experiments. This can be explained potentially using the

flame thickness argument previously presented. To compare

the relative flame thicknesses for methane and propane, a

simple method is to assume the reaction sheets are of approximately equal thickness, δ, and compare their

Ze ’ vich um ers. F r the pr p e meth e mech isms use , the y re cti s steps which re

unique are the first fuel oxidation steps. The Arrhenius reaction data from the FLUENT materials

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

Figure 3.10. Methane reaction zones at

φ=0.9, φS=0.6, L= 1 mm.

30

database indicates that the activation energy used for the propane oxidation reaction is 1.256x108 J/mol,

while for the methane reaction, the activation energy is reported as 2.0x108 J/mol. At the stoichiometric

composition in air, propane flames have a measured adiabatic flame temperature of 2257 K, and methane

flames have an adiabatic flame temperature of 2226 K [36]. So the flame temperatures for the two fuels

are approximately equal, and because the combusting gases are primarily air, variations in molecular

weight of the fuel will impact the overall molecular weight of the mixture, and thus R, by only a few

percent. Setting the unburned gas temperatures equal reduces Equation 3.1 so that:

Eq. 3.2

Fr m this re ti ship it c e expecte th t the Ze ’ vich um er for methane will be on the

order of 2/3 of that for propane, meaning that the methane flame has a thickness approximately 2/3 that of

the pr p e f me. C seque t y, the c use f the simu ti ’s i i ity t pre ict the pr p e f me

behavior could be that the characteristic length of stratification was shorter than the flame thickness. For

methane flames, which are thinner by definition, the characteristic length of stratification of 1 mm may

still be sufficiently large to avoid errors in the computation.

For these computations, flames using n-heptane fuel in air were also considered. The n-heptane

mechanism, shown in Eq. 2.8, is a single step reaction, even

simpler than those used for methane and propane. Figure 3.11

shows computed heptane flames at φ=1.4, a stratification of

φS=0.6, and characteristic length L=1 mm. The behavior of the

heptane flames at this length scale is similar to, but even more

dramatic than the propane flames. At V=70 cm/s, the central

region of the flame front becomes significantly lifted from the

burner surface, as was observed in the computations for

propane. This could again be attributed to the same flame

thickness-length scale argument, as the activation energy used

in the single-step reaction by FLUENT for this computation

was 1.256x108 J/mol, which is identical to that of the propane oxidation reaction, and the adiabatic flame

temperature at the stoichiometric composition is reported as 2265 K [36], which is on the order of those

f r pr p e meth e. Theref re, the Ze ’ vich number, and consequently the flame thickness for n-

heptane flames is on the order of those for propane flames, so both should be susceptible to similar errors

in computation at equal length scales of stratification.

V=65 cm/s

V=70 cm/s

V=75 cm/s

V=85 cm/s

Figure 3.11. N-Heptane reaction zones at

φ=1.4, φS=0.6, L= 1 mm.

31

For velocities above 70 cm/s, the exact structure of the deformed heptane flame cannot be

determined, because the liftoff becomes so severe that the flame sheet breaks and the central region of the

flame is blown off completely. This phenomenon is however most likely due to the fuel choice, and not to

the simulation method. At the stoichiometric composition, the laminar flame speeds for propane,

methane, and n-heptane are 45.6 cm/s, 43.4 cm/s, and 42.2 cm/s, respectively [36]. Because the burning

velocity of n-heptane flames is nearly 10% lower than that of the propane flames, it is possible that the

blowoff observed was merely the result of exceeding the upper limit of mixture speed at which the flame

can be stabilized at the burner surface.

3.1.3 Flame Simulation with Detailed Chemistry

Even on a qualitative level, it is apparent that there are significant shortcomings in modeling

stratified flames at short length scales using heavily reduced kinetic schemes. When the characteristic

length of the compositional stratification is on the order of the flame thickness, the reaction zone structure

predicted by the two-dimensional computation bears little or no resemblance to the true flame. In this

section, similar computations were performed, replacing the global one and two-step chemistry with the

detailed kinetics described in Chapter 2. Because the computational cost of solving detailed chemistry

was as much as 30 times greater than that of the reduced models used in this study, requiring 70-90 hours

of CPU time per case, it was not feasible to provide solutions for as wide a variety of conditions.

Computations were performed using a quad-core Intel i5 CPU (2.8GHz), and it should be noted that a

major cause of the increased computation time for the detailed chemistry was the fact that the FLUENT

solver allowed parallelized calculation on all 4 cores simultaneously, while the CHEMKIN-CFD solver is

a non-parallel code. Consequently, the few selected cases discussed in this section are intended to

demonstrate the potential of detailed kinetic models to predict stratified flame structure, and not to

provide rigorous experimental validation.

One immediate advantage to the use of detailed kinetics is that because the mechanisms solve for

the intermediate reactions which contain the hydroxyl radical, OH profiles can be extracted from the

simulation results and used for a more direct comparison with the experimental visualizations. The one

remaining caveat is that because the imaging technique used captures the OH* chemiluminescence, the

intensity is proportional to the fraction of hydroxyl radicals which are in the excited state. Ground state

radicals emit no light, so the intensity cannot be directly correlated to the radical mass fractions obtained

from the simulations. While the intensity and the radical concentration are undeniably related, other

factors such as the flame temperature and properties of the optical equipment used complicate this

relationship beyond the scope of this work. Figure 3.12 shows the computed OH profile for a propane-air

32

flame at φ=1.4, with a stratification φS=0.6, characteristic length L=1 mm, and an upstream flow speed of

75 cm/s, alongside the corresponding experimental flame image.

Recalling the flame structure predicted by the reduced kinetic model discussed in the previous

secti , it is pp re t th t the et i e chemistry sig ific t y e h ces the m e ’s i ity t pre ict

stratified flame behavior, even when the characteristic length of stratification is short. The upstream edge

of the stratified flame in the computed OH profile clearly shows a wrinkled structure with a period which

corresponds to the characteristic length of the stratification, which was also observed in the experiments,

shown in Figure 3.12b. It is also clear in the computed profile that the locations of peak OH concentration

are the regions of the flame which are closest to the burner surface, which corresponds approximately

with the regions of peak chemiluminescence emission, and was a trend observed for most of the flames

tested.

The downstream edge of the reaction zone is not well defined in the species profile, and the

region of OH concentration appears much thicker than the observed flame reaction zone. This however

could be due in large part to the fact that downstream of the reaction sheet, the gases are no longer hot

enough to excite a sufficient number of radicals from the ground state to produce visible

chemiluminescence. It is also reminded that, once formed, OH is a highly diffusive species and can

diffuse into low-temperature regions from which no OH* chemiluminescence can be expected. An

absence of emission thus does not imply that 100% of the radicals have been consumed, so the smaller

concentrations of OH in the downstream gases of the computed profile are not unreasonable.

When methane was used as the fuel, the two-step reduced model was able to adequately predict

the flame structure, although it is possible that this accuracy cannot be extended to smaller stratification

lengths based on the flame thickness considerations discussed earlier. Computation of stratified methane

flames also allowed for inspection of the OH profiles, which could not be captured experimentally with

the same high resolution as those for propane. Figure 3.13 shows the OH profile for a methane flame at

φ=0.9, φS=0.6, L= 1 mm and V=75 cm/s, along with the corresponding chemiluminscence image.

a)Computed OH profile b) OH* chemiluminescence c) Temperature profile

Figure 3.12. OH profiles for propane-air flames at φ=1.4, φS=0.6, L=1 mm, V=75cm/s

33

The computed OH profile shown in Figure 3.13a displays a significantly different structure than

that of the propane flame in Figure 3.12a. Notably, the regions of high OH radical concentration in the

methane flame are not confined to small areas within the troughs of the flame wrinkle, but instead a

substantial number of the molecules are carried downstream from the flame. This corroborates the

experimental images of stratified methane flames which showed a chemiluminscence profile that was less

defined than for propane, and showed a more uniform intensity. Again the region of visible

chemiluminescence is smaller than the region of nonzero OH concentration, which again suggests that the

downstream OH molecules are likely in the ground state and do not emit photons. The flame wrinkle is

also distinguishable on the upstream edge of the flame, and again corresponds to the period of the

compositional modulation. The contour shows that the regions of peak OH concentration do occur in the

troughs of the wrinkle, which can be seen, albeit not clearly, in the flame image as well.

To determine more confidently that the improvements in simulation accuracy for the propane

flames resulted from the use of detailed kinetics as opposed to changes in another parameter of the

simulation, a detailed calculation was performed using n-heptane fuel. The single-step mechanism for n-

heptane oxidation failed to predict the flame structure at short stratification lengths, producing a deformed

flame that was qualitatively similar to those observed for propane. In Figure 3.14, the computed OH

profile for an n-heptane flame at φ=1.4, φS=0.6, L=1 mm, and V=75 cm/s is provided. Experimental data

for n-heptane was not available.

a)Computed OH profile b) OH* chemiluminescence c) Temperature profile

Figure 3.13. OH profiles for methane-air flames at φ=0.9, φS=0.6, L=1 mm, V=75cm/s

Figure 3.14. OH profile for n-heptane-air flame at φ=1.4, φS=0.6,

L=1 mm, V=75cm/s

34

The wrinkled flame structure which is expected in this stratified configuration is readily

observable in the OH profile of Figure 3.14, in sharp contrast to the split flame front which developed at

this flow speed in the single-step reaction case. The features common to all of these computed flames are

present for n-heptane as well: the wrinkling of the flame front corresponds in period to the mixture

stratification, the regions of peak OH concentration are in the regions nearest to the stoichiometric

composition close to the burner surface, and some fraction of the OH radicals are carried downstream of

the reaction sheet. Closer observation of the high-OH concentration areas in the propane and heptane

flames shows that for propane, all but a small fraction of the radicals are consumed in the high reaction

rate zones near the burner, while the heptane flame produces a band of OH radicals slightly downstream

of the flame surface. This suggest that the either the reactions which consume the OH radical in n-heptane

combustion are slower than those in propane combustion, or that n-heptane produces a larger pool of

these radicals, which thus take longer to consume.

The final scenario considered in the detailed chemistry computations was that of the enriched

propane flame. Experiments showed that increasing the mean equivalence ratio for the stratified propane-

air flames from φ=1.4 to φ=1.7 produced visible flame front deformation, particularly at lower upstream

flow velocities, where the flame structure was observed to be similar to that of a diffusion flame. Initial

calculations using reduced chemistry were performed at this higher equivalence ratio as well, but the

predicted flame structure was similar to that of the φ=1.4 flames, as any effects of mixture enrichment

were masked by the shortcomings of the computational model. Figure 3.15 shows the OH profile for a

propane-air flame at φ=1.7, φS=0.6, L=1 mm and V=65 cm/s, as well as the experimental

chemiluminscence image.

While the use of detailed chemistry is able to capture the wrinkled structure which develops in

stratified flames at moderate mixture compositions, the model used is not able to capture the unstable

deformation which develops in very rich flames. The OH profile predicted by the computations is very

similar to that of the propane flame at φ=1.4, in that there is a clear wrinkle which is periodic with the

compositional stratification, and the OH distribution is concentrated in the areas of composition nearest to

a)Computed OH profile b) OH* chemiluminescence c)Temperature profile

Figure 3.15. OH profiles for propane-air flames at φ=1.7, φS=0.6, L=1 mm, V=65cm/s

35

the stoichiometric ratio. The only apparent difference is that a smaller fraction of the OH radicals are

transported downstream of the flame in the richer case. The experimental results show an asymmetric

deformation of the flame front which is not at all present in the simulation. In contrast to the reduced

kinetic models, which consistently over-predicted the deformation of flames which were stratified at

small length scales, the detailed model seems to have under-predicted the flame deformation in the case

of very rich mixtures. The cause of this discrepancy in the detailed kinetic model is still unclear, but

points to the need for further model development to cover a wider range of flame conditions.

3.2 Flame Liftoff Analysis

3.2.1 Flame Front Deformation with Reduced Chemistry

To this point, the flames which were not able to be simulated accurately have been simply

presented in their deformed state at the end of the computations. In this section, the development of this

deformation will be examined in the context of local flame temperature, composition, and liftoff distance.

For the purposes of this analysis, the stratified propane-air flame at φ=1.4, φS=0.6, L=1mm, and

V=75 cm/s has been selected as a demonstrative case, because results using both reduced and detailed

chemistry have been computed and the deformation in the reduced case was pronounced enough to be

easily observed without the flame completely blowing off as in the case of the n-heptane flames. Figure

3.16 shows the development of the flame front deformation at five stages of the simulation, spaced evenly

at intervals of 500 time steps, or 5 ms.

It can be seen that initially, the structure of the simulated flame corresponds to that which was

observed experimentally, and this structure remains relatively unperturbed through the first 500 time steps

of the computation. Figure 3.16b shows that a very slight lifting of the center region of the flame front is

evident once 10 ms of flow time have elapsed, which increases slowly over the next 5 ms. The lifting is

more noticeable in Figure 3.16c, and the shape of the wrinkled flame suggests, as was mentioned earlier,

that the developing structure is the superposition of the short wavelength wrinkling caused by the

compositional stratification and the long wavelength deformation triggered by the solution technique. By

the time 2000 time steps have elapsed, the beginnings of two clear deformed peaks are visible, although it

a) 500 time steps b) 1000 time steps c) 1500 time steps d) 2000 time steps e) 2500 time steps

(A) (B) (C) (D) (E)

Figure 3.16. Time evolution of reaction rate contour for propane flame at φ=1.4, φS=0.6, L=1mm, V=75 cm/s

36

should be noted at this point that the flame front still maintains symmetry about the vertical centerline of

the planar domain. At 2500 time steps, the deformation has increased in amplitude, and shows an

asymmetry which is not easily explained, given that all of the flame boundary conditions were symmetric.

A potential cause of this unstable deformation in the flame could be the inability of the reduced

kinetics to compute the increase in burning rate resulting from mixture stratification at small scales. If the

model under-predicts the rate of chemical reaction, the consumption of fuel will not be able to balance the

incoming flow of fresh mixture, causing the flame to become even richer than was intended. This

enriched flame will subsequently have a lower laminar flame speed, and to compensate, the flame front

will be stabilized at a distance further from the surface of the burner. In Figure 3.17, the same five time-

snapshots are displayed, now showing the species concentration of propane in the computational domain.

The increase in unburned fuel upstream of the flame corresponding to the flame front deformation

is not unexpected. As the flame front lifts off, the area upstream of the reaction zone grows, allowing

more fuel to accumulate before being consumed. Figure 3.18

shows a close-up view of Figure 3.17e, the fuel

concentration at the end of the simulation. A noteworthy

feature of this profile is the fact that the large deformation

peaks encompass multiple fuel zones. Both peaks have a

central lean zone enclosed by two rich zones, and

immediately upstream of the reaction zone it can be seen

that the fuel from the richer edges diffuses into the central lean region. This may be the result of the flame

being substantially lifted in these regions, allowing greater time for the reactants to diffuse upstream of

the f me. H wever, the f ct th t this iffusi ccurs c uses the “ e ” mixture t e su st ti lly richer

at the flame location than at the burner outlet, which could drive further lifting of the flame, and thus

growth of the instability.

a) 500 time steps b) 1000 time steps c) 1500 time steps d) 2000 time steps e) 2500 time steps

Figure 3.17. Time evolution of fuel concentration for propane flame at φ=1.4, φS=0.6, L=1mm, V=75 cm/s

Figure 3.18. Propane concentration after

2500 time steps

37

3.2.2 Qualitative Considerations

To evaluate the variation of the reaction rate in the computations, the time evolution of the kinetic

reaction rate of the fuel oxidation step was recorded and plotted, as shown in Figure 3.19, along with the

concentration of unburned propane. These quantities represent values which are averaged over the entire

surface of the computational domain, and weighted by the local mass flux in each cell of the grid. The

annotated points A-E correspond to the times depicted in Figure 3.16. It should be noted that because the

data in this plot represents an average, it is only accurate for the purpose of determining qualitative trends.

Observing the reaction data in Figure 3.19a, it can be seen that there is an initial spike in fuel

oxidation at the beginning of the simulation; this corresponds to the initial flame ignition event. As

described in the introduction, the computational domain is initialized in each case with air at 2000 K. The

reaction does not immediately reach its full rate because initially only a small amount of fuel has entered

the domain from the burner slots, and a finite period of time is required for a steady flame to develop.

fter 500 time steps h ve e pse , c rresp i g t p i t “ ” the p ts, the re cti h s m ve ut f

the burner slots to a stable lifted configuration, which explains the rapid increase in unburned fuel mass

fraction. Figure 3.19b shows that even after the lifted flame wrinkle has been established, the unburned

fuel mass fraction continues to rise steadily, both before and after the onset of flame front deformation,

which occurs in the vicinity f p i t “C”. Thr ugh ut the e tire ef rm ti peri , the ver ge re cti

rate remains approximately constant, despite the local flame enrichment suggested by Figure 3.18. To

gain a better understanding of the behavior of the deformed flame front, it is clear that averaged data is

a) Averaged kinetic rate of reaction b Averaged propane mass fraction

Figure 3.19. Reaction rate and fuel concentration evolution

38

insufficient, and an examination of the local flame conditions in each deformed region could provide a

clearer picture of the flame physics.

For the purpose of simple qualitative comparison, the averaged unburned fuel concentrations for

four different propane flame simulations are plotted in Figure 3.20, along with corresponding data for two

methane cases in Figure 3.21. All of the propane flames shared the conditions φS=0.6, L=1 mm. For each

of the two mean equivalence ratios considered in this study, φ=1.4 at V=75 cm/s and φ=1.7 at V=65 cm/s,

the flames were simulated once using the two-step chemistry and once using the detailed reaction

mechanism. Similarly, the methane plot is for a flame at φ=0.9, φS=0.6, L=1 mm, and V=75 cm/s,

computed once using the two-step reaction and once using the detailed mechanism.

For the two cases using the two-step global reaction model, the fuel concentration profiles show a

similar trend. It is also reasonable that the mass fraction of propane for the φ=1.7 flame was consistently

higher than its leaner counterpart, since a richer flame will propagate more slowly, and thus stabilize at a

larger liftoff height, leading to a larger upstream fuel accumulation. There is however, a stark contrast

between the behavior of the reduced models and the detailed kinetics. For the cases using detailed

chemistry, the amount of unburned fuel in the computational domain never reaches a level that is even

remotely near that of the reduced chemistry value. Moreover, after a brief fluctuation during the ignition

Figure 3.20. Averaged propane mass fractions for detailed and reduced chemistry

39

period, the fuel mass fraction remains constant for the duration of the calculation is both cases using the

detailed chemistry.

In Figure 3.21, the immediately observable feature is the lack of growth in the fuel concentration

with time for the two-step reaction model. Recall that even at a short stratification length of 1 mm, the

reduced model for methane was able to successfully predict the wrinkled structure of the stratified flame

front without any unusual deformations. The computed evolution of the fuel mass fraction for the reduced

model behaves very similarly to that of the detailed model, in that there is a brief period of fluctuation

during ignition, followed by an approximately steady-state value. In fact, the reduced model for methane

actually computed a lower steady-state mass fraction of unburned fuel than the detailed kinetics. It should

be noted at this point that similar analysis for n-heptane flames revealed their behavior to be analogous to

that of the propane flames, with a steadily growing accumulation of fuel in the single step reaction model

and a significantly lower steady-state value in the detailed kinetics model. From these observations it

appears that unburned fuel accumulation is linked to the flame front deformation which is observed when

the characteristic length of stratification is shorter than the limit of accurate computation via reduced

chemistry.

Figure 3.21. Averaged methane mass fractions for detailed and reduced chemistry

40

3.2.3 Flame Zone Analysis

Because the use of averaged data in the previous section severely limits the scope of analyses

which can be performed, this section will conduct a more quantitative comparison of the stratified flames

by focusing on the region in the immediate vicinity of the flame. A number of equally-valid methods can

be used to approximate the flame sheet location in a reacting flow. Considering only the reduced kinetics

calculations, a simple and direct method would be to examine the reaction rate contours used previously

to provide illustrations of the flame structure. The location of peak fuel oxidation corresponds very

closely to the location of the flame reaction sheet. Incidentally, the complex nature of detailed kinetic

models makes it impractical to select a single elementary reaction which can be considered the

“c m usti ” step, eve if this were fe si e, the c e es t tr ck i ivi u re cti r tes i

detailed schemes. Conversely, a convenient metric to determine flame location in the detailed kinetics

simulations is to use the location of maximum OH radical concentration, which is a natural choice given

that radical emission imaging was used in the experiments to determine the flame location. Nonetheless,

the reduced kinetic models do not account for the production or consumption of the OH radical, so again

a direct comparison is not possible.

To determine the flame location using a method that can be applied with equal confidence to all

of the computations performed, the classical theory of thermal flame structure described by Mallard and

Le Chatelier [38] will be used. This model considers the flame location in the context of temperature, and

is divided into a preheat, or conduction zone, where heat is conducted from the flame into the unburned

gases to initiate reaction, and the reaction

zone, where the infinitely thin flame sheet

resides. A schematic of the thermal flame

structure is provided in Figure 3.22. The

unburned gases enter the preheat zone at

the upstream reference temperature, T0,

and undergo a period of rapid heating due

to conduction from the downstream flame.

At the moment the gases reach the

position of the reaction sheet, they are hot

enough to ignite, and combustion occurs

in the flame zone, δ. The burned gases

reach a steady state flame temperature Tf,

and are carried downstream.

Figure 3.22. Mallard and Le Chatelier thermal flame

theory

41

This model provides a general description of the overall flame structure, with a few key

shortcomings. In the preheat zone, the classical formulation represents the temperature increase due to

heat conduction as a linear function of position, an approximation used to derive early expressions for

flame thickness and laminar flame speed. Measurement of temperature profiles in real flames however,

indicates that the relationship is non-linear, and that there is a location of peak heating in the preheat zone,

which is a fundamental component of this analysis.

The thermal formulation also assumes that the location of the flame zone is solely a function of

the temperature, that is, the ignition temperature for a given mixture is an inherent property of the

composition. Repeated efforts to catalog ignition temperatures have failed to produce consistent results

for varying flame configurations using even simple hydrocarbons, and consequently the original

expressions for flame thickness and flame speed dependent on this quantity have been reformulated to

depend on the activation energy of the reaction, in the manner of Eqs. 3.1.

This model also assumes that complete combustion is achieved in the reaction sheet, which can

only occur in the limit of infinitely-fast chemistry. Using finite-rate kinetics, which all of the mechanisms

in this study do to more realistically represent the combustion phenomenon, there will be a region of

continued radical recombination downstream of the flame. While the radical concentration downstream of

the reaction sheet is generally much lower than within it, the recombination processes are strongly

exothermic, so the temperature of the burned gases will continue to increase above the theoretical Tf

downstream of the flame [39]. This final point is significant in determining the location of the flame,

because it indicates that the reaction zone location does not correspond to the location of peak

temperature.

As mentioned previously, the combined reaction and preheat-zone flame thickness, δL is on the

order of 1 mm for most hydrocarbon flames. Because of this, determining a location well within the

preheat zone is a good approximation for the flame location, to an accuracy of < 1 mm. This location was

determined by computing the location of peak temperature increase as a function of y-displacement from

the burner surface. This region is approximately centrally located within the preheat zone of the flame,

and can be found using a simple mathematical optimization technique.

42

For the cases in which the flame front did not deform, the peak heating location was determined

using an averaged temperature distribution for the entire computational domain at a selected time step.

The static temperature at this instant was plotted against the y-displacement from the burner surface. At

each y-displacement, the temperature was determined as the arithmetic mean across the entire domain in

the x-direction at that specified height. Figure 3.23 demonstrates a temperature profile determined using

this method for a propane-air flame at φ=1.4, φS=0.6, L=1 mm and V=75 cm/s using detailed kinetics at

2500 time steps. Figure 3.23a shows a scatter of the entire temperature distribution, and 3.23b shows the

single curve that is produced by averaging.

The temperature profile shows a similarity in overall structure to the theoretical flame of Figure

3.22, with the exceptions that the temperature variation in the preheat zone is non-linear, and the

maximum temperature occurs downstream of the flame. It is also noteworthy that the temperature profile

is smooth despite the presence of a wrinkled flame, which is because the amplitude of the steady-state

wrinkle is small compared to the 0.1 mm grid resolution used in the computations. The fact that the

profile is smooth suggests that the averaged temperature approach used is an appropriate approximation

under these conditions.

Once the temperature profile was obtained, the point of peak temperature increase was

determined by differentiating the temperature curve. This was accomplished using a piecewise linear

technique, with the curve split into 56 segments spaced 0.1 mm of liftoff distance from one another,

corresponding to the node spacing of the computational grid. The absolute maximum of the derivative

could then be obtained directly, or in the case of multiple maxima, a zero-crossing analysis was

performed on the second derivative to determine the locations of relative maxima.

a) Nodal temperatures for entire domain b) Spatially-averaged temperature profile

Figure 3.23. Calculated temperature profiles for a propane flame at φ=1.4, φS=0.6, L=1mm, V=75 cm/s

with detailed kinetics

43

Figure 3.24 shows the same spatially-averaged temperature profile of Figure 3.23b, but includes

the first derivative of temperature with respect to liftoff distance overlaid on the plot, with a

corresponding scale on the right-hand

vertical axis. The derivative reaches a

clearly defined absolute maximum

near the center of the preheat zone, at

a lifted distance of 0.4 mm,

corresponding to a local temperature

of approximately 1163 K. It is

expected for a flame in this

configuration that the reaction sheet

temperature should be about 1000 K

higher than this value, indicating the

short length scale at which the

preheating of the incoming gases

occurs.

To evaluate the local mixture composition in the preheat zone, the computed peak heating

temperature was used as an iso-surface in the fuel mass fraction profile generated by the computation.

From the species concentration data

extracted, it was then possible to plot

the equivalence ratio of the mixture

along the constant-temperature line as

a function of displacement parallel to

the burner surface, X, demonstrated in

Figure 3.25. The plotted equivalence

ratio distribution clearly reflects the

sinusoidal behavior of the wrinkled

flame, which is expected since the

flame wrinkles form due to variations

in composition. Additionally, the

range of computed equivalence ratios

in the preheat zone, 0.35< φ < 0.6, indicates that by the time the gas has been heated to 1163 K, there has

already been significant reaction and diffusion of fuel into the reaction zone. Also noteworthy is that

Figure 3.24. Temperature derivative profile

Figure 3.25. Preheat zone equivalence ratio distribution

44

while the variation in composition between the fuel inlets was φS=0.6, the difference between the

computed maximum and minimum local composition in the preheat zone was only 0.26, indicating that

even for the case of the stable flame where the liftoff distance was small, substantial mixing of the

reactants occurred prior to the flame, which also partially explains the small amplitude of flame wrinkling

observed even at large stratifications. This analysis was conducted for the entire calculation at intervals

of 250 time steps, and from 500 time steps onward, when all of the transient ignition effects had been

stabilized, the computed preheat zone temperature varied by less than 1 K, and the computed local

equivalence ratios varied by less than 1/1000, indicating that the flame was steady.

While these results for the detailed kinetics simulation of the stable stratified flame provide

additional support to indicate that detailed chemistry can accurately model this phenomenon, this type of

analysis can also be used to explore the

deformed flame calculated using reduced

chemistry. The deformed flames however

present an additional set of complicating

circumstances. The spatial-averaging

technique developed for the stable flame

can be applied with reasonable results in

the early stages of the calculation, when

the flame deformation is small, but at as

the central region of the flame becomes

more lifted, the computed preheat

temperature becomes increasingly

inaccurate. In Figure 3.26, the spatially

averaged temperature profile for the deformed flame front after 2500 time steps is shown for a propane

flame under the same conditions as previously described, in this case computed with reduced chemistry.

The temperature profile no longer displays the smooth rise that was observed in the detailed kinetics case,

and two relative maxima of temperature increase are present within the preheat zone. The values of

temperature and flame liftoff reported on the plot are the result of averaging between the two computed

maxima, but this technique is not well suited for use in computing mixture composition. If the mean

preheat zone temperature is taken, the mixture composition will be computed at some locations prior to

the preheat zone, which will be nearly as rich as the inlet mixture; other locations could be very near the

local reaction sheet, where the mixture will be fuel-lean. Because the exact locations of the reaction sheet

Figure 3.26. Temperature derivative profile with reduced

chemistry

45

at each point in the domain are not known, there is no way to scale the computed composition to the

preheat zone condition using this approach, so the results would be essentially meaningless.

In order to better understand

the behavior of the deformed flame

with time, the preceding analysis was

confined to three small regions of

interest within the domain. Reducing

the size of the area considered reduces

the magnitude of the error introduced

by spatial averaging. The three regions

used are shown on a flame reaction contour in Figure 3.27. Each of the regions corresponds to one of the

inlet slots of the stratified burner. Slot 0 is the center inlet, through which the rich mixture is injected, and

the other two slots are the third and fifth slots to the right of center, respectively, and inject the lean

mixture. These regions were selected because they encapsulate three unique features of the deformed

flame front: the center lifted region, one of the large amplitude deformation peaks, and an anchored

region which remains close to the burner. For each zone, the dashed line represents the central axis used

for computation of the one-dimensional temperature distribution; no temperature averaging was

performed in this analysis. The solid boundaries of the region correspond to the edges of the inlet slot, and

enclose the area considered for equivalence ratio calculations.

Figure 3.28 shows the variation in the flame liftoff heights and computed local mean equivalence

ratios with simulation time.

Observing first the general trends in the data, it is reasonable that the regions of the flame which

Figure 3.27. Analysis zones for deformed propane flame

a) Flame liftoff variation b) Mean equivalence ratio variation

Figure 3.28. Flame liftoff distance and local equivalence ration for three flame zones

46

became substantially lifted, slots 0 and 3, have richer local composition, which supports the argument that

the liftoff is the result of decreased flame propagation rate. In addition, even prior to the onset of flame

deformation, the range of computed preheat zone equivalence ratios, 0.69 < φ < 1.05, is nearly two times

richer than that for the flame computed using detailed kinetics, supporting the hypothesis that reduced

chemistry under-predicts the rate of reaction for flames stratified at short length scales. Consequently, the

steady region of the flame in the slot 5 zone is stabilized at a liftoff height of approximately 0.8 mm,

which is approximately double that of the detailed chemistry flame.

In the fuel concentration profiles of Figures 3.17 and 3.18, it was noted that in the deformed peak

regions, there was significant observable diffusion of fuel from the rich zones at the edges of the peak to

the lean zone which formed its center. This observation is confirmed in the equivalence ratio profile,

which shows that by the end of the simulation, the mean composition of the lean zone in slot 3,

corresponding to the center of a deformed peak, is nearly equal in composition to the rich zone

corresponding to slot 0. However, the liftoff height of the slot 3 zone is significantly higher than that of

the slot 0 zone by the end of the simulation, despite the nearly identical compositions. The slot 0 zone is

bordered on both sides by leaner mixtures, so the direction of diffusion of fuel is outward into the

neighboring zones, which could have a stabilizing effect on the flame position. In contrast, the enriched

region of slot 3 is bordered on both sides by mixtures which are of equal or richer composition, further

driving the effect of the perturbation caused by local enrichment. What is unclear from this data is the

cause of this behavior. The flame is stratified uniformly in space, and yet mixing between the regions of

unlike composition occurs in a non-uniform way; damping the perturbation in some regions, while

enhancing it in others. This appears to be the primary shortcoming of the computations using reduced

kinetics. If the failing of the computation was simply to underestimate the reaction rate, it would be

expected that the predicted flame would be of similar structure to the experimental case, stabilized at a

greater liftoff distance, or that blowoff would be predicted to occur at lower velocities than

experimentally observed. Instead, the code displays inconsistent behavior even within a single flame,

where regions of the same flame front react differently to identical conditions.

An additional feature of the plots in Figure 3.28 is that there is a clearly observable delay between

a change in the local mixture composition and a corresponding change in the flame liftoff height. For the

slot 3 zone, the period of peak local enrichment occurs between time steps 1250 and 1750, during which

the mean equivalence ratio increases by 32%, but the period where the liftoff increases most rapidly does

not occur until time steps 1750-2250, during which the liftoff height increases by 40%. The observed

leveling of the liftoff profile for the slot 3 flame front at 2500 time steps is then likely the delayed

response of the flame to the leaning of the local mixture at 2000 time steps, indicating that were the

47

simulation allowed to run longer, the flame liftoff would increase further still. Similar effects are

observed for the flame front in the slot 5 region, with the flame first receding and then advancing in a

delayed response to fluctuations of the local mixture. This behavior corroborates observations for flames

propagating in time-varying mixtures, where the flame front oscillations were observed to become phase-

shifted and damped in amplitude above a certain critical frequency of compositional modulation [13]. The

flame front behavior in the region corresponding to slot 0 is unique in that the liftoff appears to increase

steadily despite the local mixture remaining approximately constant. This indicates that either the flame is

being lifted as the result of the enrichment of the neighboring regions, or that the local equivalence ratio is

simply too rich for the flame to be stabilized at a single liftoff height.

Analysis of a methane flame at φ=0.9, φs=0.6, L=1 mm, and V=75 cm/s computed using reduced

chemistry showed similar behavior to that of the propane flame using detailed kinetics, as was the case

with the previous qualitative comparisons. The preheat zone temperature remained in the range of 1245 K

to 1260K, and the liftoff was steady at 0.3 mm, noting that fluctuations in the liftoff of smaller than

0.1 mm could not be measured due to the limiting factor of grid resolution. The preheat zone equivalence

ratio varied by only small quantities and remained near φ=0.7. It is interesting to note that the liftoff

height for the methane flame was smaller than the propane flame using detailed kinetics despite a richer

mixture in the preheat zone, although this could simply be the result of more rapid diffusion of the fuel to

the reaction sheet for propane.

3.3 Flame Stretch

3.3.1 Theoretical Considerations

The concept of flame stretch was first introduced by Karlovitz [39] as a means of describing

interruptions in turbulent flame propagation. Stretch extends the concept of the Darrieus-Landau one-

dimensional hydrodynamic flame to a three-dimensional flame surface which is not necessarily planar.

The stretch rate combines the effects of flame sheet curvature with those of non-uniformity in the flow

field to describe deviations in propagation behavior from the one-dimensional model. The flame stretch

rate is defined as the specific rate of flame surface generation:

Eq. 3.3

κ is taken as the area of an infinitesimal region of the three-dimensional surface, and consequently κ is a

normalized measure of the increase in that area, and takes units of s-1

. The expression for flame stretch in

this form is not readily computed, so a generalized expression has been developed [40].

48

This expression considers a general three-dimensional flame defined in the following manner:

| | Eqs. 3.4

such that F is a function describing the location of the flame surface, v is the velocity of a particle at the

surface, n is a unit vector which is oriented normal to the surface at all points, and vn is the propagation

velocity of the flame front in the direction of n. The stretch of this flame is then defined by:

Eq. 3.5

Here V is the flow velocity vector field at the flame surface. The first term of the expression considers the

contributions of local flow field non-uniformity as well as flame surface curvature, while the second term

accounts for the stretch due to a non-stationary flame front. The following analysis will consider only

stable, stationary flames, so for the purpose of simplicity, vn is taken to be zero.

In the present work, the flame is computed in a two-dimensional planar domain, and so the

function F, which defines the stationary flame surface, reduces simply to an expression of the flame

height in terms of the burner position, y=f(x). Using this simplified formulation, the flame stretch can be

expressed explicitly in terms of the flame height and velocity field, as shown by Yokomori and Mizomoto

[41]:

(

) (

)

(

)

[(

) ]

[(

) ]

Eq. 3.6

Early attempts to characterize the effects of stretch on the flame propagation were largely

unsuccessful do to their lack of consideration of variations in the diffusive properties of dissimilar

mixtures. Corrections for the variation in diffusivities for different fuels and mixture compositions can be

made quantitatively using a nondimensional parameter known as the Lewis Number, defined as:

Eq. 3.7

where λ is the thermal conductivity of the mixture, ρu is the unburned gas density, Cp is the specific heat

of the mixture, and D is the mass diffusivity of the deficient reactant. Consequently, the Lewis Number

indicates the relative strength of thermal to molecular diffusion within the flame. The Lewis number was

also referenced in the introduction, as it governs the development of diffusive-thermal instabilities in

49

flames. For flames which are nearly equidiffusive, that is, flames with Le~1, the effects of stretching on

the burning rate and flame propagation are minimal. For flames in which Le < 1, including the rich

propane and lean methane flames considered in this study, the local flame temperature and the burning

rate vary proportionally with stretch. Reducing positive stretch, noting that κ is defined as positive in the

direction of flame propagation, reduces the flame temperature up to a critical stretch rate at which

extinction occurs [29]. Consequently, the flame propagation speed is also related to the stretch rate.

Although the details of this relation are complex, a simplified form is [42]:

Eq. 3.8

where Sf is the flame speed, Sf 0 is the laminar flame speed for the specific mixture, and α is a non-

dimensional coefficient which depends on the quantity (Le – 1). From this expression it can be seen that

the flame speed varies with stretch in a manner analogous to the temperature variation. When Le > 1, α

takes a positive value, and consequently the flame speed decreases with increasing positive stretch. The

opposite case is true for flames with Le < 1. For flames that are nearly equidiffusive, α tends to zero, and

the flame speed is virtually independent of the stretch rate.

3.3.2 Flame Stretch Computations

The computational model was able to generate values for the velocity field and local velocity

derivatives used in Eq. 3.6 at all points on the computed flame surface, and the derivatives of f(x) were

computed from the flame surface coordinates using a central-difference method. It should be noted that

these computations could only be performed with any reasonable degree of accuracy on the flames in

which a stable wrinkle developed, namely, the propane flames computed with detailed kinetics, and the

methane flames. For the flames in which large deformations developed, determination of the location of

the flame was not possible except in small local regions, as discussed previously. Splitting the flame into

individual regions is not well suited to this analysis because the stretch rate is heavily dependent on

derivative values, which develop substantial discontinuities when the initial data is segmented.

Additionally, the development of flame-front deformations in the reduced kinetics computations was

unsteady, and so the assumption of a stationary flame made to simplify Eq. 3.5 no longer holds.

Figure 3.29a illustrates the flame surface for a propane flame at an average φ=1.4, a stratification

increment φS=0.6, stratification length L=1 mm, and flow velocity V=75 cm/s, computed using detailed

kinetics, as it would appear in three-dimensional space. This highlights a critical assumption and potential

limitation of the calculations. Because the simulated flames were computed in a planar domain, the model

assumed that the surface does not vary in the depth-wise direction, which is indicated on the figure as Y.

50

Any curvature at the leading and trailing edges of the flame along the Y dimension is thus neglected. This

assumption is not entirely unreasonable however. Figure 3.29b shows a photograph of the natural flame

luminosity for a wrinkled flame of the type studied in this work, and it can be seen that the leading and

trailing edges of the flame in the direction perpendicular to the wrinkling show negligible curvature.

Figure 3.30 shows a plot of the computed stretch rate along the surface of the flame. The stretch

rate is represented by the solid line, and

its magnitude is indicated on the right-

hand vertical axis. For reference, the

cross-sectional profile of the flame

surface is presented as the dotted line,

with the flame height indicated on the

left-h xis. t th the “pe ks”

the “tr ughs” f the f me wri k e, the

structure of the flame surface is nearly

planar, and thus nearly unstretched,

which would be expected. The areas

between the rich and lean zones,

corresponding to significant changes in

the stable liftoff height of the flame,

show substantial stretching. Because

a) Projection of computed flame surface b) Wrinkled flame surface

Figure 3.29. Surface variation in computed and experimental wrinkled flames

Figure 3.30. Stretch rate for propane-air flame at an

average φ=1.4, φS=0.6, L=1mm, V=75 cm/s

51

the length scales of stratification in these experiments were very short, the changes in curvature of the

flame surface occurred over correspondingly short distances, leading to magnitudes of stretch rate which

were very large in comparison to those computed for other wrinkled laminar flames [41].

Qualitatively, the stretch rate behavior varies with the flame position in a reasonable manner. At

each peak/trough interface, there is a region where the flame is stretched and a corresponding region

where it is compressed, occurring at the inflection points of the flame surface as the local propagation

speed varies according to Eq. 3.8. There is also an apparent mirror-symmetry in the stretch behavior about

the vertical centerline of the flame. The region of maximum flame compression, which occurs just to the

right of x= -4 mm, corresponds approximately with the region of peak stretching, which occurs just to the

left of x= 4 mm. Similar mirrored pairs are observable at all of the stretched locations. Moving from left

to right, the magnitude of compression at each flame wrinkle decreases while the magnitude of stretching

increases proportionally. In fact, the maximum computed value of stretch was 2.22x105 s

-1, while the

minimum stretch (peak compression) was -2.08x105 s

-1, which is almost identical in magnitude. Taking

the mean of the stretch across all values of X yielded 1.09x103 s

-1, which is approximately 0.5% of the

peak value, and suggests although the flame is positively stretched, the wrinkled structure largely

balances the otherwise massive stretch rates.

Figure 3.31 shows the flame stretch computed identically for a propane flame at an average

φ=1.7, and V=65 cm/s with all other conditions identical to the previous case. Aside from the single peaks

of stretch and compression which are

observable in corresponding locations

along the flame, the enriched propane

flame generally shows smaller

magnitudes of stretching. The nature of

these two peaks raises some doubts as

to whether they are indicative of an

actual physical phenomenon. Unlike

the peaks in the previous plot, which

displayed finite rising and falling rates

with increasing X, the large peaks in

Figure 3.31 exist only as single points,

which suggests that they could simply

be numerical artifacts. Moreover, the

general flattening of the stretch rate

Figure 3.31. Stretch rate for propane-air flame at an

average φ=1.7, φS=0.6, L=1mm, V=65 cm/s

52

profile with increasing average equivalence ratio is consistent with the theory described in the previous

section. For propane air mixtures which are fuel-rich, further enrichment drives the flame farther from the

equidiffusive condition, that is, the Lewis Number becomes increasingly smaller than unity. Because the

mixtures are fuel-rich, the Lewis Numbers for these flames are based on the diffusivity of oxygen. For the

φ=1.4 flame, the Lewis Number was approximately 0.88, and for the φ=1.7 flame it was approximately

0.65, a decrease of roughly 25%. From Eq. 3.8, the coefficient α increases in magnitude with a

corresponding decrease in Le, reflecting the increased impact of stretching on the flame speed. The flame

in this case then has a larger, in this case meaning more negative, α, but is held stationary in a flow field

in which the flow velocity is 13% slower. For this to be the case, the stretching of the enriched flame

should be weaker than that of the leaner flame, since the increase in flame propagation speed due to

stretching is amplified. This conclusion is supported by taking the mean value of the stretch for the

enriched flame, which was 523 s-1

, or roughly half that of the previous case, which is roughly proportional

to the variation in flow speed compared to the variation in Lewis Number.

Figure 3.32 shows the computed stretch rate for a methane flame at an average φ=0.9, a

stratification increment φS=0.6, stratification length L=1 mm, and flow velocity V=75 cm/s. One

immediately notable feature of this profile as compared to the propane flames is its lack of symmetry. It is

also notable that the significant peaks of flame stretch have magnitudes which are roughly a power of ten

smaller than those for the propane flames. For lean methane-air flames, similar to rich propane-air flames,

the Lewis Number of the mixture is

smaller than one; however in this case

it was computed to be approximately

1.3, because this flame includes a

crossing of the stoichiometric ratio, and

the richer mixture has an equivalence

ratio of 1.2. Because the values of the

mass diffusivity used to compute the

Lewis number tend to be very small, Le

is very sensitive to small changes in

this property. For the two mixtures

used in this flame, the mass diffusivity

of methane was 1.5 times larger in the

rich mixture than in the lean, which

heavily weights the computed mean

Figure 3.32. Stretch rate for methane-air flame at an

average φ=0.9, φS=0.6, L=1mm, V=75 cm/s

53

toward the rich value. The fact that the equivalence ratio crosses unity at multiple locations within the

flame also makes it difficult to draw conclusions on the effects of flame stretching, although there is a

clear increase in the stretch rate at the inflection points of the flame surface, as expected.

54

Chapter 4: Conclusions and Recommendations

4.1 Concluding Remarks

4.1.1 Stratified Flame Structure

By introducing a periodic stratification of the air-fuel mixture composition at a small length scale,

it is possible to create a stable, wrinkled flame front with two steady liftoff heights determined by the

equivalence ratios of the incoming mixtures. It was observed experimentally that these flames could be

created for both methane and propane fuels at a substantial range of flow velocities, even when the length

scale of the mixture stratification was on the order of the flame thickness. Experimental results indicated

that the period of the flame front wrinkle which developed corresponded to the period of the stratification,

and that the wrinkle grew in amplitude with increased increment of stratification, or with enrichment of

the average flame composition. Conversely, increases in the upstream mixture flow velocity had a

damping effect on the wrinkling, driving the flames back toward a planar configuration. When the

average mixture composition was sufficiently fuel-rich, the wrinkling in the flame front grew very large

in amplitude, and the period no longer matched the mixture modulation. The extreme case of this was

observed for very rich propane flames in relatively slow flow fields, where it was no longer possible to

distinguish the location of the flame reaction zone, and instead the burning resembled the plume structure

of a diffusion flame. Again however, increasing the upstream flow velocity caused the flame to take on an

increasingly planar form. Additionally, increasing the increment of mixture stratification in these heavily

enriched cases appeared to stabilize the flame in the wrinkled configuration at lower velocities than for

comparable homogeneous flames. By capturing the radical chemiluminescence emitted by the flames, it

was possible to compare qualitatively the locations of maximum chemical reaction for each condition. In

all of the experimental cases where a wrinkled flame was observed, the maximum rate of reaction was

clearly located i the “tr ugh” regi s f the f me, which c rresp e t c mixture c sest i

composition to the stoichiometric ratio.

To better understand the mechanisms controlling the formation and behavior of wrinkled

stratified flames, a two-dimensional computational model was developed. The first iteration of the model

utilized global one and two-step reduced chemical kinetics with the goal of minimizing the required

computation time. It became rapidly apparent, however, that the simple mechanisms which are described

by reduced kinetics were insufficient to accurately model a stratified flame, particularly when the length

scale of the stratification became small. For propane-air and n-heptane-air flames, the reduced kinetics

simulations produced flames which suffered from large-amplitude, long-wavelength deformations which

55

increased in intensity with increasing flow field velocity, a result which directly contradicts the wrinkle-

damping effect of higher flow speeds observed experimentally. This effect was only observable when the

stratification length was 1 mm; at L=2 mm the predicted flames showed reasonable agreement with the

experiments, with the exception that the trend of wrinkle amplitude was to increase slightly with

increasing flow velocity in the simulations. For methane-air flames, the heavily reduced kinetics were

able to accurately reproduce the experimentally observed flames, at least on a qualitative level, even when

the stratification length scale was reduced to 1mm. Further exploration of this apparent inconsistency in

model performance led to the conclusion that stratified flames can be reproduced computationally with

reduced kinetics so long as the characteristic length of the stratification exceeds the laminar flame

thickness. When reduced kinetics are employed, the flame is treated as a hydrodynamic entity, which

from the classical theory is considered to be a reaction sheet of zero thickness. Because real flames have

finite thicknesses however, the classical models break down at length scales smaller than the flame

thickness, where kinetic effects dominate the flame behavior. Incidentally, the model was able to compute

the stratified methane flames to a decent degree of accuracy because methane flames are thin compared to

propane and n-heptane flames, so a stratification length scale of 1 mm was not smaller than the flame

thickness.

To increase the predictive capabilities of the computational model at small length scales of

stratification, the reduced kinetics were replaced with detailed mechanisms, which increased the number

of reactions considered from a previous maximum of 3 to as many as 308. Implementation of these

detailed chemical models allowed for accurate reproduction of both propane and n-heptane flames of

moderate average equivalence ratios even at a stratification length of 1 mm. The large scale deformations

which were created in the first iteration of the model were no longer observed, supporting the previous

conclusion that reduced kinetic models fail at length scales below the flame thickness. However, even

with detailed chemical kinetics, the simulations were not able to fully capture the behavior of very rich

propane flames, which burned in a near-diffusion mode in the experiments. The computed flames had a

stable wrinkled structure which was very similar to that of the non-enriched flames. The reasoning for the

failure of the model in these circumstances is still unclear.

4.1.2 Flame Liftoff Variation

A more detailed examination of the deformed structures produced by the reduced kinetics models

suggested that a potential mechanism driving the flame front deformation was under-prediction of the

local chemical reaction rate in the stratified regions, leading to accumulation of unburned fuel and

subsequent enrichment of the local mixture. Examination of the variation of fuel mass fraction contours in

56

a deformed propane flame with time indicated that in the highest-lifted regions of the flame, the rich

mixture had diffused substantially into the leaner one, driving the flame front farther from the burner

surface. Comparisons of domain-averaged values of fuel mass fractions between the simulations

performed with reduced and detailed chemistry revealed that the reduced kinetics models failed to reach a

steady state concentration of unburned fuel. Instead, the concentration of fuel in the domain increased at a

steady rate, both before and after the onset of flame-front deformation, indicating that the computed

chemical reaction was unable to balance the incoming mass flux of fuel.

Because averaged quantities cannot provide accurate data beyond a qualitative comparison, a

more detailed analysis of the mixture composition in the immediate vicinity of the flame was performed.

The location of the flame front in the computational domain was estimated to be a surface of constant

temperature corresponding to the location of the peak temperature increase with respect to vertical

displacement from the burner surface. While this location is actually in the preheat zone of a real flame,

and is upstream of the reaction sheet, it provides an adequate estimate of the flame location to an accuracy

of less than 1 mm. For the stable wrinkled flames produced by the computations using detailed kinetics,

this technique was able to provide a reasonable description of the composition and structure for the entire

flame. It was noted that the mixture in the preheat zone was substantially leaner than the incoming

mixture, indicating significant fuel dissociation and diffusion prior to the location of the reaction sheet.

For the flames computed using reduced kinetics which developed large deformations,

determination of the flame front location could only be performed with any degree of accuracy in small

regions, due to the large variations in the flame structure. It was observed that the liftoff height of the

flame varied proportionally with the local mixture composition, although the response was time-delayed

by a finite amount. Additionally, analysis of the composition in the region of highest deformation

supported the qualitative observation that significant enrichment of the local flame front occurs at the

peaks of the deformation. By the end of the simulation time, the local composition of the lean mixture

zone at the center of the deformed region was nearly identical in composition to that of a rich mixture

zone in a less deformed region of the flame. It was also noted that the evolution of the local mixture

composition occurred non-uniformly at different locations along the flame front, despite the fact that the

stratification imposed at the inlets was uniform and periodic.

4.1.3 Flame Stretch Rates

To further investigate the dynamics of stratified wrinkled flames, the variation in the local stretch

rate along the flame surface was determined from computational data. While stretch is typically

associated with a non-uniform velocity field upstream of the flame, the results showed that variation of

57

the local composition could lead to strong stretching. More specifically, the flame front was essentially

unstretched in the peaks and troughs of the wrinkled structure, where the surface was nearly planar, and

the magnitude of stretch became very large in the regions where the two dissimilar mixtures interacted.

The propane flames showed net positive stretching, which is consistent with their observed stability in

flow velocities exceeding the laminar flame speed of the mixture. It was difficult to draw any clear

conclusions related to the effects of stretching on the methane flames used in this study, because the

mixture compositions selected created a periodic crossing of the stoichiometric composition within the

flame front. Because stretch effects are strongly dependent on the flame Lewis Number, which is in turn a

function of the equivalence ratio, stretch analysis becomes difficult when the flame is not fully rich or

fully lean.

4.2 Recommendations for Further Study

The results presented in this work are intended to provide the preliminary groundwork for further

study of wrinkled stratified flames. The experimental flame imaging techniques used were limited in

scope and unable to yield significant quantitative data. A better understanding of the variation of the

reaction rate within the wrinkled flames could be determined using a laser-induced fluorescence method.

This technique has two primary advantages: it allows for the excitation of a specific radical or molecule in

the flame, eliminating the uncertainty in the observed emission of natural luminosity, and it allows the

input light intensity to be controlled explicitly, so quantitative analyses of the emitted intensity are

possible. Furthermore, the current understanding of the flow field upstream of the flame in the stratified

burner is limited to a few simplifying assumptions and the velocity field computed by numerical

modeling in which idealized boundary conditions were imposed. A direct study of the flow behavior in

the burner using a technique such as particle image velocimetry would provide a detailed picture of the

flow field, and indicate any shortcomings in the assumptions used.

The experiments performed were limited in their scope to methane and propane flames, and

considered only a small range of possible configurations. The behavior of different fuels, notably those

which are not alkanes, could differ significantly from the existing results. Even for the two alkane fuels

selected, the full extent of velocity and mixture limits for flame stability was not explored. Propane

studies were largely restricted to rich flames, where the development of the wrinkled structure was most

readily observed, and it is possible that stratification could have a different effect on very lean flames. At

the very rich limit, large increments of stratification were found to stabilize the flame structure, and

investigation into the ability of stratification to extend rich flammability limits could potentially yield

interesting results.

58

The computational model in its present state has many aspects which warrant further

development. Using the existing model with reduced kinetics, an alternate mesh could be explored where

the length scale of the compositional stratification is shorter than 1 mm, which is not only difficult to

realize experimentally, but would allow for the methane flame to be examined at a stratification length on

the order of its flame thickness. This could provide further validation to the argument explaining the

inaccuracies of the model for propane and n-heptane flames. Even with the implementation of relatively

detailed kinetics, the model employed is still highly idealized. The species limitations imposed by the

chemistry solver do not permit a full study of the effects of the mechanism complexity on the stratified

flame behavior. Moreover, the physics of the model are not entirely realistic. The planar model does not

account for flame surface variation in the direction perpendicular to the inlet slots, and an extension of the

model to a full three-dimensional flame surface would be beneficial. A three dimensional burner model

could also be used to study flames which are stratified in two dimensions, creating a more complex

wrinkled structure.

The thermal conditions imposed at the boundaries of the domain are idealized to constant

temperature or constant heat flux conditions. These are rather unrealistic, particularly in the case of the

burner surface being modeled at constant temperature. At small scales, the behavior of burner-stabilized

flames is strongly dependent on heat loss to the burner itself, which acts as a large thermal sink relative to

the flame size. Radiation is also neglected, which is only a reasonable assumption for a select few

hydrocarbon flames, particularly methane. Most hydrocarbons, such as propane, produce appreciable

amounts of soot, and luminous soot oxidation leads to high radiation losses. The difficulty in improving

these boundary conditions is determining appropriate values of the heat transfer parameters. Radiation

properties can be estimated based on the components of the mixture and its optical density, and an

experimental technique such as infrared imaging could be used to estimate conduction heating of the

burner top.

The consideration of the local stretch effects presented in this work represents only a small

fraction of the flame dynamics analysis which could be performed on these stratified flames. Detailed

theory exists which could be used to perform a full stability analysis of the flames based on both their

physical and chemical characteristics, although it would be a mathematically intense undertaking due to

their non-planar nature.

59

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62

Appendix A: Kinetic Mechanisms Used in Computations

A.1 Propane_NOx_HighT Mechanism

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!! Detailed Mechanism for Propane Combustion with NOx !!!

!!! Reaction Design, 2009 by Naik, C. V. !!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

ELEMENTS

H C O N

END

SPECIES

H H2 O O2 OH

H2O CO HCO CO2

CH3 HO2 H2O2 CH2O CH3O

C2H4 CH2 C2H C2H2 HCCO

C3H4-A C3H4-P C3H6 NC3H7 IC3H7

C3H8 CH3O2 CH3O2H C3H5-A C3H3

C3H2 CH2(S) HOCHO N NNH

NO CH3NO

N2

END

REACTIONS MOLES CAL/MOLE

CH3O2+HO2=CH3O2H+O2 2.5E11 0.0 -1.57E3

NC3H7+O2=C3H6+HO2 1.71E42 -9.211 1.979E4

IC3H7+O2=C3H6+HO2 3.9E48 -11.002 2.1249E4

CH3+O2=CH3O+O 1.375E13 0.0 3.052E4

CH3+O2=CH2O+OH 5.87E11 0.0 1.424E4

CH3+O2(+M)=CH3O2(+M) 1.006E8 1.63 0.0E0

LOW/3.816E31 -4.89E0 3.432E3/

TROE/4.5E-2 8.801E2 2.5E9 1.786E9/

CH3O2+CH3=2CH3O 9.0E12 0.0 -1.2E3

CH3+HO2=CH3O+OH 1.5E13 0.0 0.0E0

CH3O(+M)=CH2O+H(+M) 6.8E13 0.0 2.617E4

H2/2.0/

H2O/6.0/

CO/1.5/

CO2/2.0/

LOW/1.867E25 -3.0E0 2.4307E4/

TROE/9.0E-1 2.5E3 1.3E3 1.0E99/

CO+O2=CO2+O 2.53E12 0.0 4.77E4

HCO+OH=CO+H2O 3.02E13 0.0 0.0E0

HCO+HO2=CH2O+O2 2.97E10 0.33 -3.861E3

O+H2=H+OH 5.08E4 2.67 6.292E3

O+H2O=2OH 2.97E6 2.02 1.34E4

OH+H2=H+H2O 2.16E8 1.51 3.43E3

H2O2+OH=H2O+HO2 1.0E12 0.0 0.0E0

DUP

C2H4+O=CH3+HCO 1.02E7 1.88 1.79E2

CO+O(+M)=CO2(+M) 1.8E10 0.0 2.384E3

63

H2/2.5/

H2O/12.0/

CO/1.9/

CO2/3.8/

LOW/1.35E24 -2.788E0 4.191E3/

HCO+O=CO+OH 3.02E13 0.0 0.0E0

CH2O+M=HCO+H+M 6.283E29 -3.57 9.32E4

CH2O+OH=HCO+H2O 3.43E9 1.18 -4.47E2

CH2O+H=HCO+H2 9.334E8 1.5 2.976E3

CH2O+O=HCO+OH 4.16E11 0.57 2.762E3

CH3+OH=CH2O+H2 2.25E13 0.0 4.3E3

CH3+O=CH2O+H 8.0E13 0.0 0.0E0

C2H4(+M)=C2H2+H2(+M) 1.8E13 0.0 7.6E4

LOW/1.5E15 0.0E0 5.5443E4/

HO2+O=OH+O2 3.25E13 0.0 0.0E0

CH3O+O2=CH2O+HO2 5.5E10 0.0 2.424E3

HCO+O2=CO+HO2 7.58E12 0.0 4.1E2

HO2+H=2OH 7.08E13 0.0 3.0E2

HO2+H=H2+O2 1.66E13 0.0 8.2E2

2HO2=H2O2+O2 4.2E14 0.0 1.198E4

DUP

H2O2(+M)=2OH(+M) 2.95E14 0.0 4.84E4

H2/2.5/

H2O/12.0/

CO/1.9/

CO2/3.8/

LOW/1.27E17 0.0E0 4.55E4/

TROE/5.0E-1 1.0E-30 1.0E30/

H2O2+H=H2O+OH 2.41E13 0.0 3.97E3

CH2O+HO2=HCO+H2O2 5.82E-3 4.53 6.557E3

O+H+M=OH+M 4.72E18 -1.0 0.0E0

H2/2.5/

H2O/12.0/

CO/1.9/

CO2/3.8/

2O+M=O2+M 6.17E15 -0.5 0.0E0

H2/2.5/

H2O/12.0/

CO/1.9/

CO2/3.8/

H2+M=2H+M 4.57E19 -1.4 1.044E5

H2/2.5/

H2O/12.0/

CO/1.9/

CO2/3.8/

H+C2H(+M)=C2H2(+M) 1.0E17 -1.0 0.0E0

H2/2.0/

H2O/6.0/

CO/1.5/

CO2/2.0/

LOW/3.75E33 -4.8E0 1.9E3/

TROE/6.464E-1 1.32E2 1.315E3 5.566E3/

C2H2+O2=HCCO+OH 2.0E8 1.5 3.01E4

CH2+O2=CO+H2O 7.28E19 -2.54 1.809E3

64

C2H2+OH=C2H+H2O 3.37E7 2.0 1.4E4

O+C2H2=C2H+OH 3.16E15 -0.6 1.5E4

C2H2+O=CH2+CO 6.12E6 2.0 1.9E3

C2H+O2=HCO+CO 2.41E12 0.0 0.0E0

CH2+O2=HCO+OH 1.29E20 -3.3 2.84E2

CH2+O=CO+2H 5.0E13 0.0 0.0E0

CH2+O2=CO2+2H 3.29E21 -3.3 2.868E3

H2O2+O=OH+HO2 9.55E6 2.0 3.97E3

C2H2+O=HCCO+H 1.43E7 2.0 1.9E3

CH2+O2=CH2O+O 3.29E21 -3.3 2.868E3

HCCO+OH=2HCO 1.0E13 0.0 0.0E0

HCCO+H=CH2(S)+CO 1.1E14 0.0 0.0E0

HCCO+O=>H+2CO 8.0E13 0.0 0.0E0

CH2+O2=CO2+H2 1.01E21 -3.3 1.508E3

C2H2+CH3=C3H4-P+H 1.211E17 -1.2 1.668E4

C3H5-A=C2H2+CH3 2.397E48 -9.9 8.208E4

C2H2+CH3=C3H4-A+H 6.74E19 -2.08 3.159E4

C3H6+HO2=C3H5-A+H2O2 1.5E11 0.0 1.419E4

C3H6+OH=C3H5-A+H2O 3.12E6 2.0 -2.98E2

CH2O+M=CO+H2+M 1.826E32 -4.42 8.712E4

NC3H7=CH3+C2H4 2.284E14 -0.55 2.84E4

NC3H7=H+C3H6 2.667E15 -0.64 3.682E4

C3H6+O=C3H5-A+OH 5.24E11 0.7 5.884E3

C3H6+H=C3H5-A+H2 1.73E5 2.5 2.492E3

C3H6+H=C2H4+CH3 4.83E33 -5.81 1.85E4

IC3H7=H+C3H6 8.569E18 -1.57 4.034E4

C3H8+O2=IC3H7+HO2 4.0E13 0.0 4.75E4

C3H8+O2=NC3H7+HO2 4.0E13 0.0 4.75E4

H+C3H8=H2+IC3H7 1.3E6 2.4 4.471E3

H+C3H8=H2+NC3H7 1.88E5 2.75 6.28E3

C3H8+O=IC3H7+OH 2.81E13 0.0 5.2E3

C3H8+O=NC3H7+OH 1.13E14 0.0 7.85E3

C3H8+OH=NC3H7+H2O 1.054E10 0.97 1.586E3

C3H8+OH=IC3H7+H2O 4.67E7 1.61 -3.5E1

C3H8+HO2=IC3H7+H2O2 5.6E12 0.0 1.77E4

C3H8+HO2=NC3H7+H2O2 1.68E13 0.0 2.043E4

IC3H7+C3H8=NC3H7+C3H8 3.0E10 0.0 1.29E4

C3H8+C3H5-A=IC3H7+C3H6 2.0E11 0.0 1.61E4

C3H8+C3H5-A=NC3H7+C3H6 7.94E11 0.0 2.05E4

H2O2+H=H2+HO2 6.03E13 0.0 7.95E3

HCO+O=CO2+H 3.0E13 0.0 0.0E0

H+CH2(+M)=CH3(+M) 6.0E14 0.0 0.0E0

H2/2.0/

H2O/6.0/

CO/1.5/

CO2/2.0/

LOW/1.04E26 -2.76E0 1.6E3/

TROE/5.62E-1 9.1E1 5.836E3 8.552E3/

CH3+H=CH2+H2 9.0E13 0.0 1.51E4

CH3+OH=CH2+H2O 3.0E6 2.0 2.5E3

2HO2=H2O2+O2 1.3E11 0.0 -1.629E3

DUP

CH3O2H=CH3O+OH 6.31E14 0.0 4.23E4

C3H2+O2=>HCCO+CO+H 5.0E13 0.0 0.0E0

65

CH3O2+CH2O=CH3O2H+HCO 1.99E12 0.0 1.167E4

H2O2+OH=H2O+HO2 5.8E14 0.0 9.56E3

DUP

2CH3O2=O2+2CH3O 1.4E16 -1.61 1.86E3

C3H6+CH3O2=C3H5-A+CH3O2H 3.24E11 0.0 1.49E4

CH3+OH=CH2(S)+H2O 2.65E13 0.0 2.186E3

CH3O2+C3H8=CH3O2H+NC3H7 1.7E13 0.0 2.046E4

CH3O2+C3H8=CH3O2H+IC3H7 2.0E12 0.0 1.7E4

C3H4-A+HO2=>C2H4+CO+OH 1.0E12 0.0 1.4E4

C3H4-A+HO2=C3H3+H2O2 3.0E13 0.0 1.4E4

C3H6+O2=C3H5-A+HO2 4.0E12 0.0 3.99E4

C3H5-A+H=C3H4-A+H2 1.81E13 0.0 0.0E0

C3H4-A+C3H6=2C3H5-A 8.391E17 -1.29 3.369E4

C3H4-A+M=C3H3+H+M 1.143E17 0.0 7.0E4

C3H4-A=C3H4-P 1.202E15 0.0 9.24E4

C3H4-A+O2=C3H3+HO2 4.0E13 0.0 3.916E4

C3H3+H=C3H2+H2 5.0E13 0.0 0.0E0

C3H4-A+OH=C3H3+H2O 1.0E7 2.0 1.0E3

C3H4-A+O=C2H4+CO 7.8E12 0.0 1.6E3

C3H2+OH=C2H2+HCO 5.0E13 0.0 0.0E0

C3H5-A=C3H4-A+H 6.663E15 -0.43 6.322E4

C3H4-A+H=C3H3+H2 2.0E7 2.0 5.0E3

C3H4-A+C3H5-A=C3H3+C3H6 2.0E11 0.0 7.7E3

C3H4-A+C2H=C3H3+C2H2 1.0E13 0.0 0.0E0

C3H4-P+M=C3H3+H+M 1.143E17 0.0 7.0E4

C3H4-P=C2H+CH3 4.2E16 0.0 1.0E5

C3H4-P+O2=C3H3+HO2 2.0E13 0.0 4.16E4

C3H4-P+HO2=>C2H4+CO+OH 3.0E12 0.0 1.9E4

C3H4-P+OH=C3H3+H2O 1.0E7 2.0 1.0E3

C3H4-P+O=C3H3+OH 7.65E8 1.5 8.6E3

C3H4-P+O=HCCO+CH3 9.6E8 1.0 0.0E0

C3H4-P+H=C3H3+H2 2.0E7 2.0 5.0E3

C3H4-P+C2H=C3H3+C2H2 1.0E12 0.0 0.0E0

C3H4-P+C3H5-A=C3H3+C3H6 1.0E12 0.0 7.7E3

C3H3+O=CH2O+C2H 1.0E13 0.0 0.0E0

C3H3+OH=C3H2+H2O 1.0E13 0.0 0.0E0

C3H5-A+O2=C3H4-A+HO2 2.18E21 -2.85 3.076E4

C3H5-A+O2=>C2H2+CH2O+OH 9.72E29 -5.71 2.145E4

HCCO+O2=CO2+HCO 2.4E11 0.0 -8.54E2

C2H4+H2=2CH3 3.767E12 0.83 8.471E4

IC3H7+OH=C3H6+H2O 2.41E13 0.0 0.0E0

HOCHO+OH=>H2O+CO2+H 2.62E6 2.06 9.16E2

HOCHO+OH=>H2O+CO+OH 1.85E7 1.51 -9.62E2

HOCHO+H=>H2+CO2+H 4.24E6 2.1 4.868E3

HOCHO+H=>H2+CO+OH 6.03E13 -0.35 2.988E3

HOCHO+HO2=>H2O2+CO+OH 1.0E12 0.0 1.192E4

HOCHO+O=>CO+2OH 1.77E18 -1.9 2.975E3

CH2(S)+M=CH2+M 1.0E13 0.0 0.0E0

CH2(S)+H2=CH3+H 7.0E13 0.0 0.0E0

CH2(S)+O=CO+2H 3.0E13 0.0 0.0E0

CH2(S)+OH=CH2O+H 3.0E13 0.0 0.0E0

CH2(S)+CO2=CH2O+CO 3.0E12 0.0 0.0E0

CH2(S)+CH3=C2H4+H 2.0E13 0.0 0.0E0

C3H5-A+CH2O=C3H6+HCO 6.3E8 1.9 1.819E4

66

C3H5-A+OH=C3H4-A+H2O 6.03E12 0.0 0.0E0

CH2+O=HCO+H 8.0E13 0.0 0.0E0

CH2+OH=CH2O+H 2.0E13 0.0 0.0E0

CH2+HO2=CH2O+OH 2.0E13 0.0 0.0E0

2CH2=C2H2+H2 3.2E13 0.0 0.0E0

CH2(S)+O=CO+H2 1.5E13 0.0 0.0E0

CH2(S)+O=HCO+H 1.5E13 0.0 0.0E0

CH3+CH2=C2H4+H 4.0E13 0.0 0.0E0

CH3+HCCO=C2H4+CO 5.0E13 0.0 0.0E0

CH3+C2H=C3H3+H 2.41E13 0.0 0.0E0

CH3O+H=CH2O+H2 2.0E13 0.0 0.0E0

CH3O+H=CH3+OH 3.2E13 0.0 0.0E0

CH3O+H=CH2(S)+H2O 1.6E13 0.0 0.0E0

CH3O+O=CH2O+OH 1.0E13 0.0 0.0E0

CH3O+OH=CH2O+H2O 5.0E12 0.0 0.0E0

C2H+OH=H+HCCO 2.0E13 0.0 0.0E0

C2H+H2=H+C2H2 4.9E5 2.5 5.6E2

HCCO+O2=>OH+2CO 1.6E12 0.0 8.54E2

2HCCO=>C2H2+2CO 1.0E13 0.0 0.0E0

C2H2+OH=CH3+CO 4.83E-4 4.0 -2.0E3

C2H2+CH2=C3H3+H 1.2E13 0.0 6.62E3

C2H2+CH2(S)=C3H3+H 2.0E13 0.0 0.0E0

C2H2+HCCO=C3H3+CO 1.0E11 0.0 3.0E3

C2H4+O=CH2+CH2O 3.84E5 1.83 2.2E2

C2H4+CH2=C3H5-A+H 2.0E13 0.0 6.0E3

C2H4+CH2(S)=C3H5-A+H 5.0E13 0.0 0.0E0

C3H2+H=C3H3 1.0E13 0.0 0.0E0

C3H2+O=C2H2+CO 6.8E13 0.0 0.0E0

C3H3+HCO=C3H4-A+CO 2.5E13 0.0 0.0E0

C3H3+HCO=C3H4-P+CO 2.5E13 0.0 0.0E0

C3H4-P+H=C3H4-A+H 6.27E17 -0.91 1.0079E4

C3H4-P+H=C3H5-A 4.91E60 -14.37 3.1644E4

C3H4-P+C3H3=C3H4-A+C3H3 6.14E6 1.74 1.045E4

C3H4-P+O=C2H4+CO 1.0E13 0.0 2.25E3

C3H5-A+HCO=C3H6+CO 6.0E13 0.0 0.0E0

IC3H7+H(+M)=C3H8(+M) 2.4E13 0.0 0.0E0

H2/2.0/

H2O/6.0/

CO/1.5/

CO2/2.0/

LOW/1.7E58 -1.208E1 1.1264E4/

TROE/6.49E-1 1.2131E3 1.2131E3 1.337E4/

IC3H7+H=C3H6+H2 3.2E12 0.0 0.0E0

IC3H7+HCO=C3H8+CO 1.2E14 0.0 0.0E0

NC3H7+H(+M)=C3H8(+M) 3.6E13 0.0 0.0E0

H2/2.0/

H2O/6.0/

CO/1.5/

CO2/2.0/

LOW/3.01E48 -9.32E0 5.8336E3/

TROE/4.98E-1 1.314E3 1.314E3 5.0E4/

NC3H7+H=C3H6+H2 1.8E12 0.0 0.0E0

NC3H7+OH=C3H6+H2O 2.4E13 0.0 0.0E0

NC3H7+HCO=C3H8+CO 6.0E13 0.0 0.0E0

67

CH3O2+H2O2=CH3O2H+HO2 1.32E4 2.5 9.56E3

HOCHO+M=CO+H2O+M 2.3E13 0.0 5.0E4

HOCHO+M=CO2+H2+M 1.5E16 0.0 5.7E4

HCO+OH=HOCHO 1.0E14 0.0 0.0E0

HO2+H=O+H2O 3.97E12 0.0 6.71E2

H+O2=O+OH 1.97E14 0.0 1.654E4

CO+OH=CO2+H 7.046E4 2.053 -3.5567E2

DUP

CO+OH=CO2+H 5.757E12 -0.664 3.3183E2

DUP

HCO+M=CO+H+M 1.87E17 -1.0 1.7E4

H2/2.0/

H2O/12.0/

CO/1.75/

CO2/3.6/

H+O2(+M)=HO2(+M) 5.12E12 0.44 0.0E0

O2/0.85/

H2O/11.89/

CO/1.09/

CO2/2.18/

LOW/6.328E19 -1.4E0 0.0E0/

TROE/5.0E-1 1.0E-30 1.0E30/

H+OH+M=H2O+M 4.4E22 -2.0 0.0E0

H2/0.73/

CO/1.9/

CO2/3.8/

CH2(S)+O2=>H+OH+CO 2.8E13 0.0 0.0E0

CH2(S)+O2=CO+H2O 1.2E13 0.0 0.0E0

CO+HO2=CO2+OH 1.57E5 2.18 1.7943E4

OH+HO2=H2O+O2 6.67E28 -4.73 5.503E3

DUP

OH+HO2=H2O+O2 2.51E12 2.0 4.0E4

DUP

HCO+H=CO+H2 1.2E14 0.0 0.0E0

C3H5-A+H(+M)=C3H6(+M) 2.0E14 0.0 0.0E0

H2/2.0/

H2O/6.0/

CO/1.5/

CO2/2.0/

LOW/1.33E60 -1.2E1 5.9678E3/

TROE/2.0E-2 1.0966E3 1.0966E3 6.8595E3/

NO+CH3(+M)=CH3NO(+M) 9.0E12 0.0 1.92E2

LOW/2.5E16 0.0E0 -2.841E3/

TROE/5.0E0 1.0E-30 1.2E2 1.0E30/

N+OH=NO+H 3.36E13 0.0 3.85E2

N+O2=NO+O 9.0E9 1.0 6.5E3

N+NO=N2+O 2.7E13 0.0 3.55E2

NNH=N2+H 6.5E7 0.0 0.0E0

NNH+H=N2+H2 1.0E14 0.0 0.0E0

NNH+O=N2+OH 8.0E13 0.0 0.0E0

NNH+OH=N2+H2O 5.0E13 0.0 0.0E0

NNH+O2=N2+HO2 2.0E14 0.0 0.0E0

NNH+O2=N2+H+O2 5.0E13 0.0 0.0E0

END

68

A.2 Modified GRI 3.0 Methane Mechanism

! 12/8/08 CVN removed Ar, C3H8, C3H7

!

! GRI-Mech Version 3.0 7/30/99 CHEMKIN format

! See README30 file at anonymous FTP site unix.sri.com, directory gri;

! WorldWideWeb home page http://www.me.berkeley.edu/gri_mech/ or

! through http://www.gri.org , under 'Basic Research',

! for additional information, contacts, and disclaimer

ELEMENTS

O H C N

END

SPECIES

H2 H O O2 OH H2O HO2 H2O2

C CH CH2 CH2(S) CH3 CH4 CO CO2

HCO CH2O CH2OH CH3O CH3OH C2H C2H2 C2H3

C2H4 C2H5 C2H6 HCCO CH2CO HCCOH N NH

NH2 NH3 NNH NO NO2 N2O HNO CN

HCN H2CN HCNN HCNO HOCN HNCO NCO

!AR C3H7 C3H8

CH2CHO CH3CHO N2

END

!THERMO

! Insert GRI-Mech thermodynamics here or use in default file

!END

REACTIONS

2O+M<=>O2+M 1.200E+17 -1.000 .00

H2/ 2.40/ H2O/15.40/ CH4/ 2.00/ CO/ 1.75/ CO2/ 3.60/ C2H6/ 3.00/ !AR/

.83/

O+H+M<=>OH+M 5.000E+17 -1.000 .00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

O+H2<=>H+OH 3.870E+04 2.700 6260.00

O+HO2<=>OH+O2 2.000E+13 .000 .00

O+H2O2<=>OH+HO2 9.630E+06 2.000 4000.00

O+CH<=>H+CO 5.700E+13 .000 .00

O+CH2<=>H+HCO 8.000E+13 .000 .00

O+CH2(S)<=>H2+CO 1.500E+13 .000 .00

O+CH2(S)<=>H+HCO 1.500E+13 .000 .00

O+CH3<=>H+CH2O 5.060E+13 .000 .00

O+CH4<=>OH+CH3 1.020E+09 1.500 8600.00

O+CO(+M)<=>CO2(+M) 1.800E+10 .000 2385.00

LOW/ 6.020E+14 .000 3000.00/

H2/2.00/ O2/6.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/3.50/ C2H6/3.00/ !AR/

.50/

O+HCO<=>OH+CO 3.000E+13 .000 .00

O+HCO<=>H+CO2 3.000E+13 .000 .00

O+CH2O<=>OH+HCO 3.900E+13 .000 3540.00

O+CH2OH<=>OH+CH2O 1.000E+13 .000 .00

O+CH3O<=>OH+CH2O 1.000E+13 .000 .00

O+CH3OH<=>OH+CH2OH 3.880E+05 2.500 3100.00

O+CH3OH<=>OH+CH3O 1.300E+05 2.500 5000.00

O+C2H<=>CH+CO 5.000E+13 .000 .00

O+C2H2<=>H+HCCO 1.350E+07 2.000 1900.00

69

O+C2H2<=>OH+C2H 4.600E+19 -1.410 28950.00

O+C2H2<=>CO+CH2 6.940E+06 2.000 1900.00

O+C2H3<=>H+CH2CO 3.000E+13 .000 .00

O+C2H4<=>CH3+HCO 1.250E+07 1.830 220.00

O+C2H5<=>CH3+CH2O 2.240E+13 .000 .00

O+C2H6<=>OH+C2H5 8.980E+07 1.920 5690.00

O+HCCO<=>H+2CO 1.000E+14 .000 .00

O+CH2CO<=>OH+HCCO 1.000E+13 .000 8000.00

O+CH2CO<=>CH2+CO2 1.750E+12 .000 1350.00

O2+CO<=>O+CO2 2.500E+12 .000 47800.00

O2+CH2O<=>HO2+HCO 1.000E+14 .000 40000.00

H+O2+M<=>HO2+M 2.800E+18 -.860 .00

O2/ .00/ H2O/ .00/ CO/ .75/ CO2/1.50/ C2H6/1.50/ N2/ .00/ !AR/ .00/

H+2O2<=>HO2+O2 2.080E+19 -1.240 .00

H+O2+H2O<=>HO2+H2O 11.26E+18 -.760 .00

H+O2+N2<=>HO2+N2 2.600E+19 -1.240 .00

!H+O2+AR<=>HO2+AR 7.000E+17 -.800 .00

H+O2<=>O+OH 2.650E+16 -.6707 17041.00

2H+M<=>H2+M 1.000E+18 -1.000 .00

H2/ .00/ H2O/ .00/ CH4/2.00/ CO2/ .00/ C2H6/3.00/ !AR/ .63/

2H+H2<=>2H2 9.000E+16 -.600 .00

2H+H2O<=>H2+H2O 6.000E+19 -1.250 .00

2H+CO2<=>H2+CO2 5.500E+20 -2.000 .00

H+OH+M<=>H2O+M 2.200E+22 -2.000 .00

H2/ .73/ H2O/3.65/ CH4/2.00/ C2H6/3.00/ !AR/ .38/

H+HO2<=>O+H2O 3.970E+12 .000 671.00

H+HO2<=>O2+H2 4.480E+13 .000 1068.00

H+HO2<=>2OH 0.840E+14 .000 635.00

H+H2O2<=>HO2+H2 1.210E+07 2.000 5200.00

H+H2O2<=>OH+H2O 1.000E+13 .000 3600.00

H+CH<=>C+H2 1.650E+14 .000 .00

H+CH2(+M)<=>CH3(+M) 6.000E+14 .000 .00

LOW / 1.040E+26 -2.760 1600.00/

TROE/ .5620 91.00 5836.00 8552.00/

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+CH2(S)<=>CH+H2 3.000E+13 .000 .00

H+CH3(+M)<=>CH4(+M) 13.90E+15 -.534 536.00

LOW / 2.620E+33 -4.760 2440.00/

TROE/ .7830 74.00 2941.00 6964.00 /

H2/2.00/ H2O/6.00/ CH4/3.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+CH4<=>CH3+H2 6.600E+08 1.620 10840.00

H+HCO(+M)<=>CH2O(+M) 1.090E+12 .480 -260.00

LOW / 2.470E+24 -2.570 425.00/

TROE/ .7824 271.00 2755.00 6570.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+HCO<=>H2+CO 7.340E+13 .000 .00

H+CH2O(+M)<=>CH2OH(+M) 5.400E+11 .454 3600.00

LOW / 1.270E+32 -4.820 6530.00/

TROE/ .7187 103.00 1291.00 4160.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

H+CH2O(+M)<=>CH3O(+M) 5.400E+11 .454 2600.00

LOW / 2.200E+30 -4.800 5560.00/

TROE/ .7580 94.00 1555.00 4200.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

70

H+CH2O<=>HCO+H2 5.740E+07 1.900 2742.00

H+CH2OH(+M)<=>CH3OH(+M) 1.055E+12 .500 86.00

LOW / 4.360E+31 -4.650 5080.00/

TROE/ .600 100.00 90000.0 10000.0 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

H+CH2OH<=>H2+CH2O 2.000E+13 .000 .00

H+CH2OH<=>OH+CH3 1.650E+11 .650 -284.00

H+CH2OH<=>CH2(S)+H2O 3.280E+13 -.090 610.00

H+CH3O(+M)<=>CH3OH(+M) 2.430E+12 .515 50.00

LOW / 4.660E+41 -7.440 14080.0/

TROE/ .700 100.00 90000.0 10000.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

H+CH3O<=>H+CH2OH 4.150E+07 1.630 1924.00

H+CH3O<=>H2+CH2O 2.000E+13 .000 .00

H+CH3O<=>OH+CH3 1.500E+12 .500 -110.00

H+CH3O<=>CH2(S)+H2O 2.620E+14 -.230 1070.00

H+CH3OH<=>CH2OH+H2 1.700E+07 2.100 4870.00

H+CH3OH<=>CH3O+H2 4.200E+06 2.100 4870.00

H+C2H(+M)<=>C2H2(+M) 1.000E+17 -1.000 .00

LOW / 3.750E+33 -4.800 1900.00/

TROE/ .6464 132.00 1315.00 5566.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+C2H2(+M)<=>C2H3(+M) 5.600E+12 .000 2400.00

LOW / 3.800E+40 -7.270 7220.00/

TROE/ .7507 98.50 1302.00 4167.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+C2H3(+M)<=>C2H4(+M) 6.080E+12 .270 280.00

LOW / 1.400E+30 -3.860 3320.00/

TROE/ .7820 207.50 2663.00 6095.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+C2H3<=>H2+C2H2 3.000E+13 .000 .00

H+C2H4(+M)<=>C2H5(+M) 0.540E+12 .454 1820.00

LOW / 0.600E+42 -7.620 6970.00/

TROE/ .9753 210.00 984.00 4374.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+C2H4<=>C2H3+H2 1.325E+06 2.530 12240.00

H+C2H5(+M)<=>C2H6(+M) 5.210E+17 -.990 1580.00

LOW / 1.990E+41 -7.080 6685.00/

TROE/ .8422 125.00 2219.00 6882.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H+C2H5<=>H2+C2H4 2.000E+12 .000 .00

H+C2H6<=>C2H5+H2 1.150E+08 1.900 7530.00

H+HCCO<=>CH2(S)+CO 1.000E+14 .000 .00

H+CH2CO<=>HCCO+H2 5.000E+13 .000 8000.00

H+CH2CO<=>CH3+CO 1.130E+13 .000 3428.00

H+HCCOH<=>H+CH2CO 1.000E+13 .000 .00

H2+CO(+M)<=>CH2O(+M) 4.300E+07 1.500 79600.00

LOW / 5.070E+27 -3.420 84350.00/

TROE/ .9320 197.00 1540.00 10300.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

OH+H2<=>H+H2O 2.160E+08 1.510 3430.00

2OH(+M)<=>H2O2(+M) 7.400E+13 -.370 .00

LOW / 2.300E+18 -.900 -1700.00/

TROE/ .7346 94.00 1756.00 5182.00 /

71

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

2OH<=>O+H2O 3.570E+04 2.400 -2110.00

OH+HO2<=>O2+H2O 1.450E+13 .000 -500.00

DUPLICATE

OH+H2O2<=>HO2+H2O 2.000E+12 .000 427.00

DUPLICATE

OH+H2O2<=>HO2+H2O 1.700E+18 .000 29410.00

DUPLICATE

OH+C<=>H+CO 5.000E+13 .000 .00

OH+CH<=>H+HCO 3.000E+13 .000 .00

OH+CH2<=>H+CH2O 2.000E+13 .000 .00

OH+CH2<=>CH+H2O 1.130E+07 2.000 3000.00

OH+CH2(S)<=>H+CH2O 3.000E+13 .000 .00

OH+CH3(+M)<=>CH3OH(+M) 2.790E+18 -1.430 1330.00

LOW / 4.000E+36 -5.920 3140.00/

TROE/ .4120 195.0 5900.00 6394.00/

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

OH+CH3<=>CH2+H2O 5.600E+07 1.600 5420.00

OH+CH3<=>CH2(S)+H2O 6.440E+17 -1.340 1417.00

OH+CH4<=>CH3+H2O 1.000E+08 1.600 3120.00

OH+CO<=>H+CO2 4.760E+07 1.228 70.00

OH+HCO<=>H2O+CO 5.000E+13 .000 .00

OH+CH2O<=>HCO+H2O 3.430E+09 1.180 -447.00

OH+CH2OH<=>H2O+CH2O 5.000E+12 .000 .00

OH+CH3O<=>H2O+CH2O 5.000E+12 .000 .00

OH+CH3OH<=>CH2OH+H2O 1.440E+06 2.000 -840.00

OH+CH3OH<=>CH3O+H2O 6.300E+06 2.000 1500.00

OH+C2H<=>H+HCCO 2.000E+13 .000 .00

OH+C2H2<=>H+CH2CO 2.180E-04 4.500 -1000.00

OH+C2H2<=>H+HCCOH 5.040E+05 2.300 13500.00

OH+C2H2<=>C2H+H2O 3.370E+07 2.000 14000.00

OH+C2H2<=>CH3+CO 4.830E-04 4.000 -2000.00

OH+C2H3<=>H2O+C2H2 5.000E+12 .000 .00

OH+C2H4<=>C2H3+H2O 3.600E+06 2.000 2500.00

OH+C2H6<=>C2H5+H2O 3.540E+06 2.120 870.00

OH+CH2CO<=>HCCO+H2O 7.500E+12 .000 2000.00

2HO2<=>O2+H2O2 1.300E+11 .000 -1630.00

DUPLICATE

2HO2<=>O2+H2O2 4.200E+14 .000 12000.00

DUPLICATE

HO2+CH2<=>OH+CH2O 2.000E+13 .000 .00

HO2+CH3<=>O2+CH4 1.000E+12 .000 .00

HO2+CH3<=>OH+CH3O 3.780E+13 .000 .00

HO2+CO<=>OH+CO2 1.500E+14 .000 23600.00

HO2+CH2O<=>HCO+H2O2 5.600E+06 2.000 12000.00

C+O2<=>O+CO 5.800E+13 .000 576.00

C+CH2<=>H+C2H 5.000E+13 .000 .00

C+CH3<=>H+C2H2 5.000E+13 .000 .00

CH+O2<=>O+HCO 6.710E+13 .000 .00

CH+H2<=>H+CH2 1.080E+14 .000 3110.00

CH+H2O<=>H+CH2O 5.710E+12 .000 -755.00

CH+CH2<=>H+C2H2 4.000E+13 .000 .00

CH+CH3<=>H+C2H3 3.000E+13 .000 .00

CH+CH4<=>H+C2H4 6.000E+13 .000 .00

72

CH+CO(+M)<=>HCCO(+M) 5.000E+13 .000 .00

LOW / 2.690E+28 -3.740 1936.00/

TROE/ .5757 237.00 1652.00 5069.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

CH+CO2<=>HCO+CO 1.900E+14 .000 15792.00

CH+CH2O<=>H+CH2CO 9.460E+13 .000 -515.00

CH+HCCO<=>CO+C2H2 5.000E+13 .000 .00

CH2+O2=>OH+H+CO 5.000E+12 .000 1500.00

CH2+H2<=>H+CH3 5.000E+05 2.000 7230.00

2CH2<=>H2+C2H2 1.600E+15 .000 11944.00

CH2+CH3<=>H+C2H4 4.000E+13 .000 .00

CH2+CH4<=>2CH3 2.460E+06 2.000 8270.00

CH2+CO(+M)<=>CH2CO(+M) 8.100E+11 .500 4510.00

LOW / 2.690E+33 -5.110 7095.00/

TROE/ .5907 275.00 1226.00 5185.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

CH2+HCCO<=>C2H3+CO 3.000E+13 .000 .00

CH2(S)+N2<=>CH2+N2 1.500E+13 .000 600.00

!CH2(S)+AR<=>CH2+AR 9.000E+12 .000 600.00

CH2(S)+O2<=>H+OH+CO 2.800E+13 .000 .00

CH2(S)+O2<=>CO+H2O 1.200E+13 .000 .00

CH2(S)+H2<=>CH3+H 7.000E+13 .000 .00

CH2(S)+H2O(+M)<=>CH3OH(+M) 4.820E+17 -1.160 1145.00

LOW / 1.880E+38 -6.360 5040.00/

TROE/ .6027 208.00 3922.00 10180.0 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

CH2(S)+H2O<=>CH2+H2O 3.000E+13 .000 .00

CH2(S)+CH3<=>H+C2H4 1.200E+13 .000 -570.00

CH2(S)+CH4<=>2CH3 1.600E+13 .000 -570.00

CH2(S)+CO<=>CH2+CO 9.000E+12 .000 .00

CH2(S)+CO2<=>CH2+CO2 7.000E+12 .000 .00

CH2(S)+CO2<=>CO+CH2O 1.400E+13 .000 .00

CH2(S)+C2H6<=>CH3+C2H5 4.000E+13 .000 -550.00

CH3+O2<=>O+CH3O 3.560E+13 .000 30480.00

CH3+O2<=>OH+CH2O 2.310E+12 .000 20315.00

CH3+H2O2<=>HO2+CH4 2.450E+04 2.470 5180.00

2CH3(+M)<=>C2H6(+M) 6.770E+16 -1.180 654.00

LOW / 3.400E+41 -7.030 2762.00/

TROE/ .6190 73.20 1180.00 9999.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

2CH3<=>H+C2H5 6.840E+12 .100 10600.00

CH3+HCO<=>CH4+CO 2.648E+13 .000 .00

CH3+CH2O<=>HCO+CH4 3.320E+03 2.810 5860.00

CH3+CH3OH<=>CH2OH+CH4 3.000E+07 1.500 9940.00

CH3+CH3OH<=>CH3O+CH4 1.000E+07 1.500 9940.00

CH3+C2H4<=>C2H3+CH4 2.270E+05 2.000 9200.00

CH3+C2H6<=>C2H5+CH4 6.140E+06 1.740 10450.00

HCO+H2O<=>H+CO+H2O 1.500E+18 -1.000 17000.00

HCO+M<=>H+CO+M 1.870E+17 -1.000 17000.00

H2/2.00/ H2O/ .00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/

HCO+O2<=>HO2+CO 13.45E+12 .000 400.00

CH2OH+O2<=>HO2+CH2O 1.800E+13 .000 900.00

CH3O+O2<=>HO2+CH2O 4.280E-13 7.600 -3530.00

C2H+O2<=>HCO+CO 1.000E+13 .000 -755.00

73

C2H+H2<=>H+C2H2 5.680E+10 0.900 1993.00

C2H3+O2<=>HCO+CH2O 4.580E+16 -1.390 1015.00

C2H4(+M)<=>H2+C2H2(+M) 8.000E+12 .440 86770.00

LOW / 1.580E+51 -9.300 97800.00/

TROE/ .7345 180.00 1035.00 5417.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

C2H5+O2<=>HO2+C2H4 8.400E+11 .000 3875.00

HCCO+O2<=>OH+2CO 3.200E+12 .000 854.00

2HCCO<=>2CO+C2H2 1.000E+13 .000 .00

N+NO<=>N2+O 2.700E+13 .000 355.00

N+O2<=>NO+O 9.000E+09 1.000 6500.00

N+OH<=>NO+H 3.360E+13 .000 385.00

N2O+O<=>N2+O2 1.400E+12 .000 10810.00

N2O+O<=>2NO 2.900E+13 .000 23150.00

N2O+H<=>N2+OH 3.870E+14 .000 18880.00

N2O+OH<=>N2+HO2 2.000E+12 .000 21060.00

N2O(+M)<=>N2+O(+M) 7.910E+10 .000 56020.00

LOW / 6.370E+14 .000 56640.00/

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .625/

HO2+NO<=>NO2+OH 2.110E+12 .000 -480.00

NO+O+M<=>NO2+M 1.060E+20 -1.410 .00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

NO2+O<=>NO+O2 3.900E+12 .000 -240.00

NO2+H<=>NO+OH 1.320E+14 .000 360.00

NH+O<=>NO+H 4.000E+13 .000 .00

NH+H<=>N+H2 3.200E+13 .000 330.00

NH+OH<=>HNO+H 2.000E+13 .000 .00

NH+OH<=>N+H2O 2.000E+09 1.200 .00

NH+O2<=>HNO+O 4.610E+05 2.000 6500.00

NH+O2<=>NO+OH 1.280E+06 1.500 100.00

NH+N<=>N2+H 1.500E+13 .000 .00

NH+H2O<=>HNO+H2 2.000E+13 .000 13850.00

NH+NO<=>N2+OH 2.160E+13 -.230 .00

NH+NO<=>N2O+H 3.650E+14 -.450 .00

NH2+O<=>OH+NH 3.000E+12 .000 .00

NH2+O<=>H+HNO 3.900E+13 .000 .00

NH2+H<=>NH+H2 4.000E+13 .000 3650.00

NH2+OH<=>NH+H2O 9.000E+07 1.500 -460.00

NNH<=>N2+H 3.300E+08 .000 .00

NNH+M<=>N2+H+M 1.300E+14 -.110 4980.00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

NNH+O2<=>HO2+N2 5.000E+12 .000 .00

NNH+O<=>OH+N2 2.500E+13 .000 .00

NNH+O<=>NH+NO 7.000E+13 .000 .00

NNH+H<=>H2+N2 5.000E+13 .000 .00

NNH+OH<=>H2O+N2 2.000E+13 .000 .00

NNH+CH3<=>CH4+N2 2.500E+13 .000 .00

H+NO+M<=>HNO+M 4.480E+19 -1.320 740.00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

HNO+O<=>NO+OH 2.500E+13 .000 .00

HNO+H<=>H2+NO 9.000E+11 .720 660.00

HNO+OH<=>NO+H2O 1.300E+07 1.900 -950.00

HNO+O2<=>HO2+NO 1.000E+13 .000 13000.00

CN+O<=>CO+N 7.700E+13 .000 .00

74

CN+OH<=>NCO+H 4.000E+13 .000 .00

CN+H2O<=>HCN+OH 8.000E+12 .000 7460.00

CN+O2<=>NCO+O 6.140E+12 .000 -440.00

CN+H2<=>HCN+H 2.950E+05 2.450 2240.00

NCO+O<=>NO+CO 2.350E+13 .000 .00

NCO+H<=>NH+CO 5.400E+13 .000 .00

NCO+OH<=>NO+H+CO 0.250E+13 .000 .00

NCO+N<=>N2+CO 2.000E+13 .000 .00

NCO+O2<=>NO+CO2 2.000E+12 .000 20000.00

NCO+M<=>N+CO+M 3.100E+14 .000 54050.00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

NCO+NO<=>N2O+CO 1.900E+17 -1.520 740.00

NCO+NO<=>N2+CO2 3.800E+18 -2.000 800.00

HCN+M<=>H+CN+M 1.040E+29 -3.300 126600.00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

HCN+O<=>NCO+H 2.030E+04 2.640 4980.00

HCN+O<=>NH+CO 5.070E+03 2.640 4980.00

HCN+O<=>CN+OH 3.910E+09 1.580 26600.00

HCN+OH<=>HOCN+H 1.100E+06 2.030 13370.00

HCN+OH<=>HNCO+H 4.400E+03 2.260 6400.00

HCN+OH<=>NH2+CO 1.600E+02 2.560 9000.00

H+HCN(+M)<=>H2CN(+M) 3.300E+13 .000 .00

LOW / 1.400E+26 -3.400 1900.00/

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

H2CN+N<=>N2+CH2 6.000E+13 .000 400.00

C+N2<=>CN+N 6.300E+13 .000 46020.00

CH+N2<=>HCN+N 3.120E+09 0.880 20130.00

CH+N2(+M)<=>HCNN(+M) 3.100E+12 .150 .00

LOW / 1.300E+25 -3.160 740.00/

TROE/ .6670 235.00 2117.00 4536.00 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ 1.0/

CH2+N2<=>HCN+NH 1.000E+13 .000 74000.00

CH2(S)+N2<=>NH+HCN 1.000E+11 .000 65000.00

C+NO<=>CN+O 1.900E+13 .000 .00

C+NO<=>CO+N 2.900E+13 .000 .00

CH+NO<=>HCN+O 4.100E+13 .000 .00

CH+NO<=>H+NCO 1.620E+13 .000 .00

CH+NO<=>N+HCO 2.460E+13 .000 .00

CH2+NO<=>H+HNCO 3.100E+17 -1.380 1270.00

CH2+NO<=>OH+HCN 2.900E+14 -.690 760.00

CH2+NO<=>H+HCNO 3.800E+13 -.360 580.00

CH2(S)+NO<=>H+HNCO 3.100E+17 -1.380 1270.00

CH2(S)+NO<=>OH+HCN 2.900E+14 -.690 760.00

CH2(S)+NO<=>H+HCNO 3.800E+13 -.360 580.00

CH3+NO<=>HCN+H2O 9.600E+13 .000 28800.00

CH3+NO<=>H2CN+OH 1.000E+12 .000 21750.00

HCNN+O<=>CO+H+N2 2.200E+13 .000 .00

HCNN+O<=>HCN+NO 2.000E+12 .000 .00

HCNN+O2<=>O+HCO+N2 1.200E+13 .000 .00

HCNN+OH<=>H+HCO+N2 1.200E+13 .000 .00

HCNN+H<=>CH2+N2 1.000E+14 .000 .00

HNCO+O<=>NH+CO2 9.800E+07 1.410 8500.00

HNCO+O<=>HNO+CO 1.500E+08 1.570 44000.00

HNCO+O<=>NCO+OH 2.200E+06 2.110 11400.00

75

HNCO+H<=>NH2+CO 2.250E+07 1.700 3800.00

HNCO+H<=>H2+NCO 1.050E+05 2.500 13300.00

HNCO+OH<=>NCO+H2O 3.300E+07 1.500 3600.00

HNCO+OH<=>NH2+CO2 3.300E+06 1.500 3600.00

HNCO+M<=>NH+CO+M 1.180E+16 .000 84720.00

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

HCNO+H<=>H+HNCO 2.100E+15 -.690 2850.00

HCNO+H<=>OH+HCN 2.700E+11 .180 2120.00

HCNO+H<=>NH2+CO 1.700E+14 -.750 2890.00

HOCN+H<=>H+HNCO 2.000E+07 2.000 2000.00

HCCO+NO<=>HCNO+CO 0.900E+13 .000 .00

CH3+N<=>H2CN+H 6.100E+14 -.310 290.00

CH3+N<=>HCN+H2 3.700E+12 .150 -90.00

NH3+H<=>NH2+H2 5.400E+05 2.400 9915.00

NH3+OH<=>NH2+H2O 5.000E+07 1.600 955.00

NH3+O<=>NH2+OH 9.400E+06 1.940 6460.00

NH+CO2<=>HNO+CO 1.000E+13 .000 14350.00

CN+NO2<=>NCO+NO 6.160E+15 -0.752 345.00

NCO+NO2<=>N2O+CO2 3.250E+12 .000 -705.00

N+CO2<=>NO+CO 3.000E+12 .000 11300.00

O+CH3=>H+H2+CO 3.370E+13 .000 .00

O+C2H4<=>H+CH2CHO 6.700E+06 1.830 220.00

O+C2H5<=>H+CH3CHO 1.096E+14 .000 .00

OH+HO2<=>O2+H2O 0.500E+16 .000 17330.00

DUPLICATE

OH+CH3=>H2+CH2O 8.000E+09 .500 -1755.00

CH+H2(+M)<=>CH3(+M) 1.970E+12 .430 -370.00

LOW/ 4.820E+25 -2.80 590.0 /

TROE/ .578 122.0 2535.0 9365.0 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

CH2+O2=>2H+CO2 5.800E+12 .000 1500.00

CH2+O2<=>O+CH2O 2.400E+12 .000 1500.00

CH2+CH2=>2H+C2H2 2.000E+14 .000 10989.00

CH2(S)+H2O=>H2+CH2O 6.820E+10 .250 -935.00

C2H3+O2<=>O+CH2CHO 3.030E+11 .290 11.00

C2H3+O2<=>HO2+C2H2 1.337E+06 1.610 -384.00

O+CH3CHO<=>OH+CH2CHO 2.920E+12 .000 1808.00

O+CH3CHO=>OH+CH3+CO 2.920E+12 .000 1808.00

O2+CH3CHO=>HO2+CH3+CO 3.010E+13 .000 39150.00

H+CH3CHO<=>CH2CHO+H2 2.050E+09 1.160 2405.00

H+CH3CHO=>CH3+H2+CO 2.050E+09 1.160 2405.00

OH+CH3CHO=>CH3+H2O+CO 2.343E+10 0.730 -1113.00

HO2+CH3CHO=>CH3+H2O2+CO 3.010E+12 .000 11923.00

CH3+CH3CHO=>CH3+CH4+CO 2.720E+06 1.770 5920.00

H+CH2CO(+M)<=>CH2CHO(+M) 4.865E+11 0.422 -1755.00

LOW/ 1.012E+42 -7.63 3854.0/

TROE/ 0.465 201.0 1773.0 5333.0 /

H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

O+CH2CHO=>H+CH2+CO2 1.500E+14 .000 .00

O2+CH2CHO=>OH+CO+CH2O 1.810E+10 .000 .00

O2+CH2CHO=>OH+2HCO 2.350E+10 .000 .00

H+CH2CHO<=>CH3+HCO 2.200E+13 .000 .00

H+CH2CHO<=>CH2CO+H2 1.100E+13 .000 .00

OH+CH2CHO<=>H2O+CH2CO 1.200E+13 .000 .00

76

OH+CH2CHO<=>HCO+CH2OH 3.010E+13 .000 .00

!CH3+C2H5(+M)<=>C3H8(+M) .9430E+13 .000 .00

! LOW/ 2.710E+74 -16.82 13065.0 /

! TROE/ .1527 291.0 2742.0 7748.0 /

!H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

!O+C3H8<=>OH+C3H7 1.930E+05 2.680 3716.00

!H+C3H8<=>C3H7+H2 1.320E+06 2.540 6756.00

!OH+C3H8<=>C3H7+H2O 3.160E+07 1.800 934.00

!C3H7+H2O2<=>HO2+C3H8 3.780E+02 2.720 1500.00

!CH3+C3H8<=>C3H7+CH4 0.903E+00 3.650 7154.00

!CH3+C2H4(+M)<=>C3H7(+M) 2.550E+06 1.600 5700.00

! LOW/ 3.00E+63 -14.6 18170./

! TROE/ .1894 277.0 8748.0 7891.0 /

!H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

!O+C3H7<=>C2H5+CH2O 9.640E+13 .000 .00

!H+C3H7(+M)<=>C3H8(+M) 3.613E+13 .000 .00

! LOW/ 4.420E+61 -13.545 11357.0/

! TROE/ .315 369.0 3285.0 6667.0 /

!H2/2.00/ H2O/6.00/ CH4/2.00/ CO/1.50/ CO2/2.00/ C2H6/3.00/ !AR/ .70/

!H+C3H7<=>CH3+C2H5 4.060E+06 2.190 890.00

!OH+C3H7<=>C2H5+CH2OH 2.410E+13 .000 .00

!HO2+C3H7<=>O2+C3H8 2.550E+10 0.255 -943.00

!HO2+C3H7=>OH+C2H5+CH2O 2.410E+13 .000 .00

!CH3+C3H7<=>2C2H5 1.927E+13 -0.320 .00

END

A.3 ERC N-Heptane Mechanism

elements

h c o n

end

species

nc7h16 o2 n2 co2 h2o co h2 oh h2o2 ho2 h o

ch3o ch2o hco ch2 ch3 ch4 c2h3 c2h4 c2h5 c3h4 c3h5 c3h6 c3h7

c7h15-2 c7h15o2 c7ket12 c5h11co

end

reactions

nc7h16 + h = c7h15-2 + h2 4.380e+07 2.0 4760.0

nc7h16 + oh = c7h15-2 + h2o 9.700e+09 1.3 1690.0

nc7h16 + ho2 = c7h15-2 + h2o2 1.650e+13 0.0 16950.0

nc7h16 + o2 = c7h15-2 + ho2 2.000e+15 0.0 47380.0

c7h15-2 + o2 = c7h15o2 1.560e+12 0.0 0.0

c7h15o2 + o2 = c7ket12 + oh 4.500E+14 0.0 18232.712

c7ket12 = c5h11co + ch2o + oh 9.530e+14 0.0 4.110e+4

c5h11co = c2h4 + c3h7 + co 9.84E+15 0.0 4.02E+04

c7h15-2 = c2h5 + c2h4 + c3h6 7.045E+14 0.0 3.46E+04

c3h7 = c2h4 + ch3 9.600e+13 0.0 30950.0

c3h7 = c3h6 + h 1.250e+14 0.0 36900.0

c3h6 + ch3 = c3h5 + ch4 9.000e+12 0.0 8480.0

77

c3h5 + o2 = c3h4 + ho2 6.000e+11 0.0 10000.0

c3h4 + oh = c2h3 + ch2o 1.000e+12 0.0 0.0

c3h4 + oh = c2h4 + hco 1.000e+12 0.0 0.0

ch3 + ho2 = ch3o + oh 5.000e+13 0.00 0.

ch3 + oh = ch2 + h2o 7.500e+06 2.00 5000.

ch2 + oh = ch2o + h 2.500e+13 0.00 0.

ch2 + o2 = hco + oh 4.300e+10 0.00 -500.

ch2 + o2 = co2 + h2 6.900e+11 0.00 500.

ch2 + o2 = co + h2o 2.000e+10 0.00 -1000.

ch2 + o2 = ch2o + o 5.000e+13 0.00 9000.

ch2 + o2 = co2 + h + h 1.600e+12 0.00 1000.

ch2 + o2 = co + oh + h 8.600e+10 0.00 -500.

ch3o + co = ch3 + co2 1.570e+14 0.00 11800.

co + oh = co2 + h 8.987e+07 1.38 5232.877

o + oh = o2 + h 4.000e+14 -0.50 0.

h + ho2 = oh + oh 1.700e+14 0.0 875.

oh + oh = o + h2o 6.000e+08 1.30 0.

h + o2 + m = ho2 + m 3.600e+17 -0.72 0.

h2o/21./ co2/5.0/ h2/3.3/ co/2.0/

h2o2 + m = oh + oh + m 1.000e+16 0.00 45500.

h2o/21./ co2/5.0/ h2/3.3/ co/2.0/

h2 + oh = h2o + h 1.170e+09 1.30 3626.

ho2 + ho2 = h2o2 + o2 3.000e+12 0.00 0.

ch2o + oh = hco + h2o 5.563e+10 1.095 -76.517

ch2o + ho2 = hco + h2o2 3.000e+12 0.00 8000.

hco + o2 = ho2 + co 3.300e+13 -0.40 0.

hco + m = h + co + m 1.591E+18 0.95 56712.329

ch3 + ch3o = ch4 + ch2o 4.300e+14 0.00 0.

c2h4 + oh = ch2o + ch3 6.000e+13 0.0 960.

c2h4 + oh = c2h3 + h2o 8.020e+13 0.00 5955.

c2h3 + o2 = ch2o + hco 4.000e+12 0.00 -250.

c2h3 + hco = c2h4 + co 6.034e+13 0.0 0.

c2h5 + o2 = c2h4 + ho2 2.000e+10 0.0 -2200.

ch4 + o2 = ch3 + ho2 7.900e+13 0.00 56000.

oh + ho2 = h2o + o2 7.50E+12 0.0 0.

ch3 + o2 = ch2o + oh 3.80E+11 0.0 9000.

ch4 + h = ch3 + h2 6.600e+08 1.60 10840.

ch4 + oh = ch3 + h2o 1.600e+06 2.10 2460.

ch4 + o = ch3 + oh 1.020e+09 1.50 8604.

ch4 + ho2 = ch3 + h2o2 9.000e+11 0.00 18700.

ch4 + ch2 = ch3 + ch3 4.000e+12 0.00 -570.

c3h6 = c2h3 + ch3 3.150e+15 0.0 85500.0

end